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  • On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations

     Codina Rovira, Ramon; Badia Rodriguez, Santiago I.
    Computer methods in applied mechanics and engineering
    Date of publication: 2013-08
    Journal article

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    The objective of this paper is to present a new framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.

  • Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows

     Guasch Fortuny, Oriol; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Date of publication: 2013-07
    Journal article

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    On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics  Open access

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Planas Badenas, Ramon
    Journal of computational physics
    Date of publication: 2013-02
    Journal article

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    In this work, we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation is the fact that it always converges to the physical solution, even for singular ones. A detailed set of numerical experiments have been performed in order to validate our approach.

  • Immersed stress method for fluidstructure interaction using anisotropic mesh adaptation

     Hachem, Elie; Feghali, S.; Codina Rovira, Ramon; Coupez, Thierry
    International journal for numerical methods in engineering
    Date of publication: 2013-06
    Journal article

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    This paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluidstructure interaction with complex geometry. First, a new stabilized three-field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the NavierStokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluidsolid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time-dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight.

  • Stabilized finite element formulations for solving incompressible magnetohydrodynamics.

     Planas Badenas, Ramon
    Defense's date: 2013-11-25
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
    Theses

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  • PIV Applications in Vortex Rings and Oscillatory Boundary Layers  Open access

     Mujal Colilles, Anna
    Defense's date: 2013-05-13
    Universitat Politècnica de Catalunya
    Theses

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    Particle Image Velocimetry (PIV) is one of the most used experimental techniques in fluid mechanics to obtain the velocity field of a flow. One of its most celebrated characteristics is that it does not have interference on the phenomenon of study which makes it suitable to describe qualitatively and quantitatively many phenomena either micro or macroscopic. This thesis presents the PIV technique applied to two different fluid mechanic problems: vortex rings impinging permeable boundaries and oscillatory boundary layers in the laminar-to-turbulent regime. The first part of this thesis focuses on the impingement of vortex rings towards permeable boundaries and compares the results with the interaction of a vortex ring with a solid boundary. Assuming that a vortex ring is an axisymmetric structure, 2D PIV experiments are performed over boundaries on 4 different permeabilities and a solid boundary. When a vortex approaches a solid boundary, three different phenomena are clearly visible: the vortex ring decelerates when the distance between the core and the wall is in the order of the initial diameter of the ring. At the same time, the diameter starts increasing producing a stretching effect and, finally, secondary vorticity appears after the ring has reached the minimum distance from the wall. Experimental results lead to some interesting conclusions when the permeability of the boundary increases: the deceleration of the vortex ring starts later, the diameter does not increase as much and, finally, secondary vorticity is weaker and has shorter life. The second and third part of this thesis focus on the study of oscillatory boundary layers over smooth and rough walls. Experimental measurements were conducted over smooth and two different rough beds spanning the laminar, transitional and turbulent flow regimes. A multi-camera 2D-PIV system was used in an experimental oscillatory-flow tunnel. Characteristic variables like boundary layer thickness and friction factor were computed using different methods. Results obtained experimentally in smooth wall experiments are consistent with theoretical work. For the rough wall cases different formulations have been compared. Finally, results show how the phase lead between wall velocity and free-stream velocity is better defined when the integral of momentum equation is used to estimate the friction velocity. The observed differences are highly sensitive to the zero level definition. Finally, a detailed analysis of the structures present in such oscillatory boundary layers yield to a description of four different features: vortex tubes present in oscillatory flows over smooth beds, and vortices, turbulent spots and shear layers present in oscillatory flows over rough beds. The inception of vortex tubes is consistent with the state-of-art predictors as a result of the Kelvin-Helmholtz instability. Furthermore, structures present in rough wall experiments are a little bit more complicated because their inception and evolution are clearly influenced by the position of the sediment grains forming the bed. Vortices are created behind a kink in the bed sediment profile during the wall flow reversal and are shed from the wall when flow starts its acceleration cycle. Both the vertical and horizontal evolutions of the vortex position depend on the ratio between the amplitude of oscillation and roughness of the sediment bed. Turbulent spots are defined as structures which are born vortices but lose their shape in an early stage. They follow the same trajectories as vortices but reach lower heights before dissipating. Finally, shear layers were only detected in the larger bed roughness and are described as a sum of vortices that are shed consecutively from the same sediment. These shear layers are linked to vortices during the wall flow reversal when a big vortex is formed in the same place as the shear layer.

    La tècnica experimental del Particle Image Velocimetry (PIV) és una de les més utilitzades en el món de la mecànica de fluids per obtenir el camp de velocitats en un flux. La seva no interferència en el desenvolupament del fenomen que s’estudia la fa aplicable a tot tipus de fenòmens, ja sigui micro com macroscòpics i permet estudiar qualitativa i quantitativament la dinàmica de fluids d’un fenomen particular. Aquesta tesis presenta l’aplicació del PIV a dos problemes de mecànica de fluids diferents: anells de vorticitat impactant contorns permeables i capes límit oscil•latòries dins del règim transitori. La primera part d’aquesta tesis es centra en l’estudi dels anells de vorticitat impactant contorns permeables i la seva comparació amb l’impacte del mateix anell amb una paret sòlida. Assumint que un anell de vorticitat és una estructura axisimètrica, s’han realitzat experiments PIV en 2D, en quatre contorns permeables diferents i un contorn sòlid. Quan un anell de vorticitat es mou cap a una superfície sòlida es fan presents tres fenòmens principals: la desacceleració de l’anell de vorticitat quan assoleix una distància amb la paret de l’ordre del diàmetre inicial de l’anell. Al mateix temps un augment del diàmetre produint un efecte estirament i finalment l’aparició d’un segon anell de vorticitat quan el primer anell ha assolit la distància mínima de la paret. El treball experimental aporta algunes conclusions interessants sobre l’evolució d’aquestes característiques principals a mesura que la permeabilitat del contorn d’impacte augmenta: la distància de la paret a la qual comença la desacceleració disminueix, el diàmetre de l’anell de vorticitat primari creix amb menys intensitat i finalment el segon anell de vorticitat és més dèbil i té una vida més curta. La segona i tercera part de la tesis es centren en descriure el fenomen de capa límit oscil•latòria en fluxos sobre llits llisos i rugosos. En aquesta tesis es descriuen els experiments centrats en l’estudi de la capa límit oscil•latòria sobre fons llis i dos tipus diferents de fons rugós per a un rang de Rew = 0.4.104 ~ 2.104; els experiments es centren en la transició de règim laminar a règim laminar a turbulent i utilitzen la tècnica de 2D PIV amb multicàmera aplicada a un túnel de flux oscil•latori. Algunes variables característiques com el gruix de la capa límit o el factor de fricció s’analitzen des de diferents perspectives. Els resultats obtinguts en els experiments de llit rugós coincideixen amb les prediccions realitzades per a teoria existent. Per als experiments en llit rugós diferents formulacions es comparen. Finalment els resultats mostren com la diferència de fase entre la velocitat de paret i a la velocitat del pistó que activa l’oscil•lació es defineix més bé quan es calcula a través de la integral de la quantitat de moviment. Les diferències observades amb els resultats obtinguts quan es calcula a través de la suma de tensions de Reynolds i tensions viscoses són degudes principalment a la sensibilitat d’ambdues equacions a la definició del zero d’ordenades. Per altra banda, el gruix màxim observat per la capa límit es produeix just abans de que es produeixi l’instant de velocitat zero, també anomenat fase del revers, independentment del règim del flux. Finalment es realitza un anàlisi detallat de les estructures presents en les capes límit oscil•latòries definint fins a quatre tipus diferents: tubs de vorticitat presents en fluxos oscil•latoris sobre llits llisos, vòrtexs, bursts i capes de tensió detectades en els fluxos sobre llits rugosos. L’evolució dels tubs de vorticitat coincideix amb la teoria ja publicada i són el resultat de l’aparició de la inestabilitat de Kelvin-Helmholtz. Els experiments descrits en aquesta tesis confirmen les mateixes característiques i permeten definir la vida d’aquests tubs de vorticitat. Les estructures presents en llits rugosos són una mica més complicades degut a que la seva formació i evolució està clarament influenciada per la posició dels grans de sediment que formen el fons. Els vòrtexs es creen darrere una punta en el perfil del llit de sediment durant la fase del revers prop de la paret i es separen d’aquesta quan comença el cicle d’acceleració. L’evolució tant de la posició vertical com horitzontal d’aquests vòrtexs depenen del quocient entre l’amplitud de l’oscil•lació i la rugositat del sediment. Els bursts es defineixen com a aquelles estructures que neixen sent un vòrtex però perden la forma de seguida. De fet, aquests bursts són vòrtexs de mida més petita i que apareixen en localitzacions properes en el camp de velocitats instantani. No obstant quan es realitza la mitjana en fase, la seva forma desapareix, mostrant-se com a bursts. La seva trajectòria és semblant a la dels vòrtexs prèviament descrits, però assoleixen una alçada inferior. Finalment les capes de tensió es visualitzaren només en els experiments portats a terme amb la màxima rugositat i es defineixen com una successió de vòrtexs creats en el mateix gra. Aquestes últimes estructures estan relacionades amb els vòrtexs inicialment descrits ja que aquests es formen amb les estructures romanents de la capa de tensió just quan es produeix el revers del flux. El treball presentat en aquesta tesis es basa en dos problemes de mecànica de fluids. No obstant confirma que la tècnica del PIV és aplicable a fenòmens totalment diferents.

  • A compressible lagrangian framework for the simulation of underwater implosion problems  Open access

     Kamran, Kazem
    Defense's date: 2013-06-21
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
    Theses

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    The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method [109]. A nodally perfect matched definition of the interface is used [57, 25] and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.

    El desarrollo de métodos eficientes para modelar la dinámica de implosión presenta varios desafíos. El primero es una representación eficaz de la dinámica del sistema acoplado de aire-agua. El segundo es que el método tiene que permitir una detección exacta o un seguimiento adecuado de la interfase entre ambas fases. Por último el método tiene que ser capaz de resolver cualquier choque que podría generar en el aire o en el agua, sobre todo en la última fase del colapso. Nosotros presentamos un método numérico compresible y totalmente Lagrangiano para simular la implosión bajo el agua. Tanto el aire como el agua se consideran compresibles y las ecuaciones Lagrangianos para la hidrodinámica del choque se estabilizan mediante un método multiescala que es variacionalmente consistente [109]. Se utiliza una definición de interfase que coincide perfectamente con los nodos [57, 25]. Ésta, nos facilita duplicar eficazmente las variables cinéticas como la presión y la densidad en los nodos de la interfase. Con el fin de obtener suficiente resolución alrededor de la interfase, la malla se genera de forma adaptativa y respetando la posición de la interfase. A continuación el método desarrollado se utiliza para simular la implosión bajo el agua de una burbuja cilíndrica del tamaño de un centímetro. Varios fenómenos se han capturado durante el colapso: un ciclo inmediato de colapso-crecimiento de la burbuja que ocurre en un espacio (0.3mm) y tiempo (0.1ms) bastante limitado, aparición de inestabilidades de tipo Rayleigh-Taylor en la interfase y formaron de varias ondas de choque que viajan tanto en el agua como en el aire. Después, seguimos el desarrollo del método para modelar la implosión bajo el agua de un contenedor metálico considerando una interacción monolítica de fluido y estructura. El cilindro de aluminio, que a su vez contiene aire a presión atmosférica y está rodeada de agua en alta presión, se modelando con elementos de lámina de tres nodos y sin grados de libertad de rotación. El cilindro se somete a deformaciones transitorias suficientemente rápidos y enormes hasta llegar a colapsar. Un nuevo modelo elástico de contacto sin considerar la fricción se ha desarrollado para detectar el contacto y calcular las fuerzas en el dominio discretizado entre las superficies medianas de las laminas. Dos esquemas temporales están considerados, uno es implícito utilizando el método de Bossak y otro es explícito utilizando Forward Euler. Al final los resultados de ambos casos se comparan con los resultados experimentales.

  • Nonlinear subgrid finite element models for low Mach number flows coupled with radiative heat transfer

     Avila Salinas, Matías Oscar
    Defense's date: 2012-11-16
    Universitat Politècnica de Catalunya
    Theses

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  • Premi ICREA Acadèmia

     Codina Rovira, Ramon
    Award or recognition

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  • IACM Fellow - 2012

     Codina Rovira, Ramon
    Award or recognition

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  • Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Planas Badenas, Ramon
    Date: 2012
    Report

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  • AJUT ICREA ACADEMIA 2011

     Codina Rovira, Ramon
    Participation in a competitive project

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    A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions  Open access

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon
    SIAM journal on numerical analysis
    Date of publication: 2012
    Journal article

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    A new mixed finite element approximation of Maxwell’s problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H(curl; ) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement.

  • A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes

     Baiges Aznar, Joan; Codina Rovira, Ramon; Henke, Florian; Shahmiri, S.; Wall, W. A.
    International journal for numerical methods in engineering
    Date of publication: 2012-05-04
    Journal article

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  • A third-order velocity correction scheme obtained at the discrete level

     Owen, H.; Codina Rovira, Ramon
    International journal for numerical methods in fluids
    Date of publication: 2012-05-10
    Journal article

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    Stokes, Maxwell and Darcy: a single finite element approximation for three model problems  Open access

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon
    Applied numerical mathematics
    Date of publication: 2012-04
    Journal article

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    In this work we propose stabilized finite element methods for Stokes’, Maxwell’s and Darcy’s problems that accommodate any interpolation of velocities and pressures. We briefly review the formulations we have proposed for these three problems independently in a unified manner, stressing the advantages of our approach. In particular, for Darcy’s problem we are able to design stabilized methods that yield optimal convergence both for the primal and the dual problems. In the case of Maxwell’s problem, the formulation we propose allows one to use continuous finite element interpolations that converge optimally to the continuous solution even if it is non-smooth. Once the formulation is presented for the three model problems independently, we also show how it can be used for a problem that combines all the operators of the independent problems. Stability and convergence is achieved regardless of the fact that any of these operators dominates the others, a feature not possible for the methods of which we are aware.

  • Dissipative structure and long term behavior of a finite element approximation of incompressible flows with numerical subgrid scale modeling

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Badia Rodriguez, Santiago I.
    Date of publication: 2011
    Book chapter

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  • Mesh objective modelling of cracks using continuous linear strain and displacement interpolations

     Cervera Ruiz, Miguel; Chiumenti, Michele; Codina Rovira, Ramon
    Congresso de Métodos Numéricos em Engenharia
    Presentation's date: 2011-06-15
    Presentation of work at congresses

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    Model problems in magneto-hydrodynamics: individual numerical challenges and coupling possibilities  Open access

     Codina Rovira, Ramon; Badia Rodriguez, Santiago I.; Planas Badenas, Ramon
    International Conference on Computational Methods for Coupled Problems in Science and Engineering
    Presentation's date: 2011
    Presentation of work at congresses

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    In this work we discuss two model problems appearing in magneto-hydrodynamics (MHD), namely, the so called full MHD problem and the inductionless MHD problem. The first involves as unknowns the fluid velocity and pressure, the magnetic (induction) fi eld and a pseudo-pressure introduced to impose the zero-divergence restriction of this last unknown. The building blocks of this model are the Stokes problem for the velocity and the pressure and the Maxwell problem for the magnetic field and pseudopressure. We discuss the numerical challenges of the approximation of these two model problems having in mind the need to couple them in the full problem, where additional coupling terms appear. The second model we consider is the inductionless MHD approximation. Instead of the magnetic induction and pseudo-pressure, the magnetic unknowns are now the current density and the electric potential. The building blocks are the Stokes problem for the fluid and the Darcy problem (in primal form) for the current density and electric potential. We discuss also the numerical challenges involved in the approximation of this last problem, particularly considering that it has to be coupled to the former. Once the building blocks have been analysed independently, the possibilities of dealing with the fully coupled problems are discussed. Iterative schemes that can be shown to be stable are presented in the stationary case, showing that a segregated solution for the flow and the magnetic problem is not possible. Most of the results presented are elaborated independently in previous works. Our objective in this paper is to present the di fferent problems with a unifi ed perspective.

  • Spatial approximation of the radiation transport equation using a subgrid-scale finite element method

     Ávila, Matias; Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    Computer methods in applied mechanics and engineering
    Date of publication: 2011-01
    Journal article

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  • A free surface finite element model for low Froude number mould filling problems on fixed meshes

     Coppola Owen, Angel H.; Codina Rovira, Ramon
    International journal for numerical methods in fluids
    Date of publication: 2011-07-10
    Journal article

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    The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface and the resulting flow field increases. The usual two-phase flow model provides poor results for such flow. In order to overcome the difficulties, a free surface model that applies boundary conditions at the interface accurately is used. Moreover, the use of wall laws on curved boundaries also fails in the case of low Froude number flows. To solve this second problem, we combine wall laws with ‘do nothing’ boundary conditions. A special feature of our approach is that ‘do nothing’ boundary conditions are only applied in the normal direction. These two key ingredients together with the Level Set method allow us to simulate three-dimensional mould filling problems borrowed directly from the foundry.

  • Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

     Cervera Ruiz, Miguel; Chiumenti, Michele; Codina Rovira, Ramon
    International journal for numerical methods in engineering
    Date of publication: 2011-09
    Journal article

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  • Approximation of the inductionless MHD problem using a stabilized finite element method

     Planas Badenas, Ramon; Badia Rodriguez, Santiago I.; Codina Rovira, Ramon
    Journal of computational physics
    Date of publication: 2011-04
    Journal article

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  • Approximation of the thermally coupled MHD problem using a stabilized finite element method

     Codina Rovira, Ramon; Hernandez, Noel
    Journal of computational physics
    Date of publication: 2011-02-20
    Journal article

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  • The Fixed-Mesh ALE approach for the numerical simulation of floating solids

     Baiges Aznar, Joan; Codina Rovira, Ramon; Coppola Owen, Angel H.
    International journal for numerical methods in fluids
    Date of publication: 2011-11-20
    Journal article

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  • A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon
    Applied mathematics and computation
    Date of publication: 2011-12
    Journal article

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  • Thermal coupling of fluid flow and structural response of a tunnel induced by fire

     Schrefler, Bernhard A.; Codina Rovira, Ramon; Pesavento, F.; Principe Rubio, Ricardo Javier
    International journal for numerical methods in engineering
    Date of publication: 2011-07
    Journal article

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  • Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems  Open access

     Nadukandi, Prashanth
    Defense's date: 2011-05-13
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
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    We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi: 10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045- 7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi: 10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small.

    Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion

  • The fixed-Mesh ALE method applied to multiphysics problems using stabilized formulations  Open access  awarded activity

     Baiges Aznar, Joan
    Defense's date: 2011-01-14
    Universitat Politècnica de Catalunya
    Theses

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    The finite element method is a tool very often employed to deal with the numerical simulation of multiphysics problems.Many times each of these problems can be attached to a subdomain in space which evolves in time. Fixed grid methods appear in order to avoid the drawbacks of remeshing in ALE (Arbitrary Lagrangian-Eulerian) methods when the domain undergoes very large deformations. Instead of having one mesh attached to each of the subdomains, one has a single mesh which covers the whole computational domain. Equations arising from the finite element analysis are solved in an Eulerian manner in this background mesh. In this work we present our particular approach to fixed mesh methods, which we call FM-ALE (Fixed-Mesh ALE). Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian-Eulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.We analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods. When dealing with certain physical problems, and depending on the finite element space used, the standard Galerkin finite element method fails and leads to unstable solutions. The variational multiscale method is often used to deal with this instability. We introduce a way to approximate the subgrid scales on the boundaries of the elements in a variational twoscale finite element approximation to flow problems. The key idea is that the subscales on the element boundaries must be such that the transmission conditions for the unknown, split as its finite element contribution and the subscale, hold. We then use the subscales on the element boundaries to improve transmition conditions between subdomains by introducing the subgrid scales between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid-structure interaction problems. The benefits in each case are respectively a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behaviour of the iterative algorithm to couple the fluid and the solid in fluid-structure interaction problems. We develop FELAP, a linear systems of equations solver package for problems arising from finite element analysis. The main features of the package are its capability to work with symmetric and unsymmetric systems of equations, direct and iterative solvers and various renumbering techniques. Performance is enhanced by considering the finite element mesh graph instead of the matrix graph, which allows to perform highly efficient block computations.

  • SHOCK CAPTURING FOR DISCONTINUOUS GALERKIN METHODS  Open access

     Casoni Rero, Eva
    Defense's date: 2011-10-14
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
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    Aquesta tesi doctoral proposa formulacions de Galerkin Discontinu (DG) d’alt ordre per la captura de shocks, obtenint alhora solucions altament precises per problemes de flux compressible. En les últimes dècades, la investigació en els mètodes de DG ha estat en constant creixement. L'èxit dels mètodes DG en problemes hiperbòlics ha conduit el seu desenvolupament en lleis de conservació no lineals i problemes de convecció dominant. Entre els avantatges dels mètodes DG, destaquen la seva estabilitat inherent i les propietats locals de conservació. D'altra banda, els mètodes DG estan especialment dissenyats per l’ús aproximacions d'ordre superior. De fet, en els últims anys s'ha demostrat que la resolució de problemes de convecció dominant ja no es restringeix només a elements d'ordre inferior. De fet, es necessiten models numèrics d'alta precisió per aconseguir prediccions altament fiables dins la dinàmica de fluids computacional (CFD). En aquest context es presenten i discuteixen dos tècniques de captura de shocks. En primer lloc, es presenta una tècnica novedosa i senzilla basada en la introducció d'una nova base de funcions de forma. Aquesta base té la capacitat de canviar a nivell local entre una interpolació contínua o discontínua, depenent de la suavitat de la funció que es vol aproximar. En presència de xocs, les discontinuïtats introduïdes dins l’element permeten incloure l'estabilització necessària gràcies a l’ús dels fluxos numèrics, i alhora exploten les propietats intrínsiques del mètodes DG. En conseqüència, es poden utilitzar malles grolleres amb elements d’ordre superior. Amb aquestes discretitzacions i, utilitzant el mètode proposats, els xocs queden continguts a l’interior de l’element i per tant, és possible evitar l’ús de tècniques de refinament adaptatiu de la malla, alhora que es manté la localitat i compacitat dels esquemes DG. En segon lloc, es proposa una tècnica clàssica i, aparentment simple: la introducció de la viscositat artificial. Primerament es realitza un estudi detallat per al cas unidimensional. S’obté una viscositat d’alta precisió que escala segons el valor hk amb 1 ≤ k ≤ p i essent h la mida de l’element. En conseqüència, s’obté un xoc amb amplitud del mateix ordre. Seguidament, l'estudi de la viscositat unidimensional obtenida s'extén al cas multidimensional per a malles triangulars. L'extensió es basa en la projecció de la viscositat unidimensional en unes determinades direccions espacials dins l’element. Es demostra de manera consistent que la viscositat introduïda és, com a molt, del mateix ordre que la resolució donada per la discretització espacial, és a dir, h/p. El mètode és especialment eficient per aproximacions de Galerkin discontinu d’alt ordre, per exemple p≥ 3. Les dues metodologies es validen mitjançant una àmplia selecció d’exemples numèrics. En alguns exemples, els mètodes proposats permeten una reducció en el nombre de graus de llibertat necessaris per capturar xocs acuradament de fins i tot un ordre de magnitud, en comparació amb mètodes estàndar de refinament adaptatiu amb aproximacions de baix ordre.

    This thesis proposes shock-capturing methods for high-order Discontinuous Galerkin (DG) formulations providing highly accurate solutions for compressible flows. In the last decades, research in DG methods has been very active. The success of DG in hyperbolic problems has driven many studies for nonlinear conservation laws and convection-dominated problems. Among all the advantages of DG, their inherent stability and local conservation properties are relevant. Moreover, DG methods are naturally suited for high-order approximations. Actually, in recent years it has been shown that convection-dominated problems are no longer restricted to low-order elements. In fact, highly accurate numerical models for High-Fidelity predictions in CFD are necessary. Under this rationale, two shock-capturing techniques are presented and discussed. First, a novel and simple technique based on on the introduction of a new basis of shape functions is presented. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization thanks to the numerical fluxes, thus exploiting DG inherent properties. Large high-order elements can therefore be used and shocks are captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Second, a classical and, apparently simple, technique is advocated: the introduction of artificial viscosity. First, a one-dimensional study is perfomed. Viscosity of the order O(hk) with 1≤ k≤ p is obtained, hence inducing a shock width of the same order. Second, the study extends the accurate one-dimensional viscosity to triangular multidimensional meshes. The extension is based on the projection of the one-dimensional viscosity into some characteristic spatial directions within the elements. It is consistently shown that the introduced viscosity scales, at most, withthe DG resolutions length scales, h/p. The method is especially reliable for highorder DG approximations, say p≥3. A wide range of different numerical tests validate both methodologies. In some examples the proposed methods allow to reduce by an order of magnitude the number of degrees of freedom necessary to accurately capture the shocks, compared to standard low order h-adaptive approaches.

  • Actes dels seminaris de recerca 1r, 2n i 3r, del Departament de Mecànica de Fluids - UPC

     De Las Heras Jimenez, Salvador Augusto; Carbo Bech, Alberto Antonio; Moreno Llagostera, Hipolit; Valle, L. J.; Poeata, I.; López, J.; Torres Camara, Ricardo; Barraco Serra, Marc; Fernandez Aguado, Enrique; Escaler Puigoriol, Francesc Xavier; Hutter, J.K.; Egusquiza Estevez, Eduardo; Farhat, Mohamed; Avellan, François; Esque de los Ojos, Daniel; Dalmau Andreu, Roger; Principe Rubio, Ricardo Javier; Roe Vellve, Nuria; Codina Rovira, Ramon; Badia Rodriguez, Santiago I.; Garcia Vilchez, Mercedes; Gamez Montero, Pedro Javier; Codina Macià, Esteban; Watton, John
    Date of publication: 2011-11-01
    Book

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  • Finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales

     Codina Rovira, Ramon; Baiges Aznar, Joan
    International journal for numerical methods in engineering
    Date of publication: 2011-02-02
    Journal article

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  • A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations

     Ávila, Matias; Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Journal of computational physics
    Date of publication: 2011-09-10
    Journal article

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  • Recent MHD activities for blanket analysis at UPC

     Mas de Les Valls Ortiz, Elisabet; Fradera, Jordi; Sedano, L.A.; Codina Rovira, Ramon; Badia Rodriguez, Santiago I.; Batet Miracle, Lluis
    Reunión Anual de la Sociedad Nuclear Española
    Presentation's date: 2010
    Presentation of work at congresses

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  • The dissipative structure of variational multiscale methods for incompressible flows

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon; Henke, Florian
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-02-01
    Journal article

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    In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.

  • Resolución numérica de las ecuaciones de la magnetohidrodinámica en el proceso Czochralski para la obtención de cristales semiconductores

     HERNÁNDEZ SILVA, NOEL; Codina Rovira, Ramon
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Date of publication: 2010
    Journal article

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  • On the stabilization parameter in the subgrid scale approximation of scalar convection-diffusion-reaction equations on distorted meshes

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-04-01
    Journal article

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    In this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection–diffusion–reaction equation. The starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated. In order to incorporate the distortion of the mesh into this approximation, we transform the equation for the subgrid scale within each element to the shape-regular reference domain. The expression for the subgrid scale arises from an approximate Fourier analysis and the identification of the wave number direction where instabilities are most likely to occur. The final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation.

  • Access to the full text
    A numerical strategy to compute optical parameters in turbulent flow: application to telescopes  Open access

     Codina Rovira, Ramon; Baiges Aznar, Joan; Pérez Sánchez, Daniel; Collados, Manuel
    Computers and fluids
    Date of publication: 2010-01
    Journal article

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    We present a numerical formulation to compute optical parameters in a turbulent air flow. The basic numerical formulation is a large eddy simulation (LES) of the incompressible Navier–Stokes equations, which are approximated using a finite element method. From the time evolution of the flow parameters we describe how to compute statistics of the flow variables and, from them, the parameters that determine the quality of the visibility. The methodology is applied to estimate the optical quality around telescope enclosures.

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  • Fixed mesh methods in computational mechanics

     Codina Rovira, Ramon; Baiges Aznar, Joan
    Date of publication: 2010
    Book chapter

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  • Numerical simulation of multi-fluid flows with the Particle Finite Element Method  Open access  awarded activity

     de Mier Torrecilla, Monica
    Defense's date: 2010-06-29
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
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    La presencia simultánea de múltiples fluidos con diferentes propiedades ocurre en numerosos problemas medioambientales, procesos industriales y situaciones de la vida diaria. Algunos ejemplos son la interacción fluido-combustible en la extracción mejorada de petróleo, mezcla de polímeros, emulsiones en productos alimentarios, formación de gotas de lluvia en nubes, inyección en motores de combustión o reactores de columna de burbujas. A pesar de que los flujos de multi-fluidos son muy frecuentes, todavía suponen un reto tanto desde el punto de vista teórico como computacional. En el caso de fluidos inmiscibles, la dinámica de la interfase entre fluidos juega un papel determinante. El éxito en la simulación de estos flujos dependerá de la capacidad del método numérico de modelar con precisión la interfase y los fenómenos que tienen lugar en ella. En este trabajo nos hemos centrado en entender la principios físicos básicos de los multi-fluidos y las dificultades que aparecen en su simulación numérica. Hemos extendido el Particle Finite Element Method (PFEM) a problemas de varios fluidos diferentes con el objetivo de explotar el hecho de que los métodos lagrangianos son especialmente adecuados para el seguimiento de todo tipo de interfases. Hemos desarrollado un esquema numérico capaz de tratar grandes saltos en las propiedades físicas (densidad y viscosidad), de incluir la tensión superficial y de representar las discontinuidades de las variables del flujo. El esquema se basa en desacoplar las variables de posición de los nodos, velocidad y presión a través de la linearización de Picard y un método de segregación de la presión que tiene en cuenta las condiciones de interfase. La interfase se ha definido alineada con la malla móvil, de forma que se mantiene el salto de propiedades físicas sin suavizar a lo largo del tiempo. Además, los grados de libertad de la presión han sido duplicados en los nodos de interfase para representar la discontinuidad de esta variable debido a la tensión superficial y a la viscosidad variable, y la malla ha sido refinada cerca de la interfase para mejorar la precisión de la simulación. Hemos aplicado el esquema resultante a diversos problemas académicos y geológicos, como el sloshingde dos fluidos, extrusión de fluidos viscosos, ascensión y rotura de una burbuja dentro de una columna de líquido, mezcla de magmas y fuentes invertidas (negatively buoyant jet).

    The simultaneous presence of multiple fluids with different properties in external or internal flows is found in daily life, environmental problems, and numerous industrial processes, among many other practical situations. Examples arefluid-fuel interaction in enhanced oil recovery, blending of polymers, emulsions in food manufacturing, rain droplet formation in clouds, fuel injection in engines, and bubble column reactors, to name only a few. Although multi-fluid flows occur frequently in nature and engineering practice, they still pose a major research challenge from both theoretical and computational points of view. In the case of immiscible fluids, the dynamics of the interface between fluids plays a dominant role. The success of the simulation of such flows will depend on the ability of the numerical method to model accurately the interface and the phenomena taking place on it. In this work we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. Theinterface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations. We have applied the resulting scheme to several academic and geological problems, such as the two-fluid sloshing, extrusion of viscous fluids, bubble rise and break up, mixing of magmatic liquids and negatively buoyant jets.

  • Stabilized Finite Element Approximation of the Incompressible MHD Equations  Open access

     HERNÁNDEZ SILVA, NOEL
    Defense's date: 2010-07-12
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
    Theses

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    No es frecuente encontrar un campo donde dos ramas principales de la Física estén involucradas. La Magnetohidrodinámica es uno de tales campos debido a que involucra a la Mecánica de Fluidos y al Electromagnetismo. Aun cuando puede parecer que esas dos ramas de la Física tienen poco en común, comparten similitudes en las ecuaciones que gobiernan los fenómenos involucrados en ellas. Las ecuaciones de Navier-Stokes y las ecuaciones de Maxwell, ambas en la raíz de la Magnetohidrodinámica, tienen una condición de divergencia nula y es esta condición de divergencia nula sobre la velocidad del fluido y el campo magnético lo que origina algunos de los problemas numéricos que surgen en la modelación de los fenómenos donde el flujo de fluidos y los campos magnéticos están acoplados.El principal objetivo de este trabajo es desarrollar un algoritmo eficiente para la resolución mediante elementos finitos de las ecuaciones de la Magnetohidrodinámica de fluidos incompresibles.Para lograr esta meta, los conceptos básicos y las características de la Magnetohidrodinámica se presentan en una breve introducción informal.A continuación, se da una revisión completa de las ecuaciones de gobierno de la Magnetohidrodinámica, comenzando con las ecuaciones de Navier-Stokes y las ecuaciones de Maxwell. Se discute la aproximación que da origen a las ecuaciones de la Magnetohidrodinámica y finalmente se presentan las ecuaciones de la Magnetohidrodinámica.Una vez que las ecuaciones de gobierno de la Magnetohidrodinámica han sido definidas, se presentan los esquemas numéricos desarrollados, empezando con la linealización de las ecuaciones originales, la formulación estabilizada y finalmente el esquema numérico propuesto. En esta etapa se presenta una prueba de convergencia.Finalmente, se presentan los ejemplos numéricos desarrollados durante este trabajo.Estos ejemplos pueden dividirse en dos grupos: ejemplos numéricos de comparación y ejemplos de internes tecnológico. Dentro del primer grupo están incluidas simulaciones del flujo de Hartmann y del flujo sobre un escalón. El segundo grupo incluye simulaciones del flujo en una tobera de inyección de colada continua y el proceso Czochralski de crecimiento de cristales.

    It is not frequent to find a field where two major branches of Physics are involved. Magnetohydrodynamics is one of such fields because it involves Fluid Mechanics and Electromagnetism. Although those two branches of Physics can seem to have little in common, they share similarities in the equations that govern the phenomena involved. The Navier-Stokes equations and the Maxwell equations, both at the root of Magnetohydrodynamics, have a divergence free condition and it is this divergence free condition over the velocity of the fluid and the magnetic field what gives origin to some of the numerical problems that appear when approximating the equations that model the phenomena where fluids flow and magnetic fields are coupled.The main objective of this work is to develop an efficient finite element algorithm for the incompressible Magnetohydrodynamics equations.In order to achieve this goal the basic concepts and characteristics of Magnetohydrodynamics are presented in a brief and informal introduction.Next, a full review of the governing equations of Magnetohydrodynamics is given, staring from the Navier-Stokes equations and the Maxwell equations. The MHD approximation is discussed at this stage and the proper Magnetohydrodynamics equations for incompressible fluid are reviewed.Once the governing equations have been defined, the numerical schemes developed are presented, starting with the linearization of the original equations, the stabilization formulations and finally the numerical scheme proposed. A convergence test is shown at this stage.Finally, the numerical examples performed while this work was developed are presented. These examples can be divided in two groups: numerical benchmarks and numerical examples of technological interest. In the first group, the numerical simulations for the Hartmann flow and the flow over a step are included. The second group includes the simulation of the clogging in a continuous casting nozzle and Czochralski crystal growth process.

  • CFD Analysis of an Axial Piston Pump  Open access  awarded activity

     Kumar, Sushil
    Defense's date: 2010-07-16
    Department of Fluid Mechanics, Universitat Politècnica de Catalunya
    Theses

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    En el ámbito de la Oleohidráulica, las bombas de pistón poseen los diseños más sofisticados, de hecho, las bombas de pistones son las únicos capaces de trabajar a altas presiones, además de poseer el mejor rendimiento de todo el grupo de bombas existentes. Sin embargo, cabe señalar que todos los diseños de las bombas de pistón, se basan principalmente en la experiencia de los diseñadores, por lo tanto no existen herramientas matemáticas para optimizar el diseño de las diferentes partes de las bombas. Por otra parte, en la actualidad hay empresas como Oilgear Towler, que inserta ranuras (surcos) en los patines deslizantes y en los pistones, (dos partes principales de estas bombas), pero no hay ningún estudio científico para analizar sus ventajas o desventajas. Por lo tanto, es necesario comprender matemáticamente las ventajas y desventajas debido a la presencia de ranuras en la superficie de diferentes partes de la bomba. Hay cuatro superficies de deslizamiento en las bombas de pistones, plato inclinado patín deslizante, barrilete y placa de cierre, pistón cilindro y junta esférica entre pistón y patín deslizante. Lubricación entre estas superficies es necesaria, apareciendo por tanto fugas de fluido a bombear entre las mismas. En este proyecto, nuestro objetivo es analizar cada una de estas diferentes superficies de deslizamiento por separado para comprender su diseño y el efecto de los parámetros de diseño en el comportamiento de la bomba. Una vez se tenga un buen entendimiento de las diferentes partes de la bomba de pistones, el objetivo es modelar el comportamiento dinámico de la presión y flujo en la salida de la bomba. En concreto se ha realizado: Conjunto plato inclinado, patín deslizante – Estudio de las características estáticas y dinámicas del patín deslizante, incluyendo la ranura tallada en el patín. Las ecuaciones de Navier Stokes en coordenadas cilíndricas se han aplicado entre el patín y el plato incluyendo la ranura. Los resultados presentados en este trabajo contemplan, distribución de la presión, las fugas de fluido, la fuerza y par sobre el patín, se ha estudiado la variación de dichos parámetros al modificar las dimensiones y posición de la ranura. El comportamiento dinámico del patín se ha tenido también en cuenta. Se estudia la posición de la ranura con el fin de optimizar el comportamiento del patín. Barrilete, placa de cierre.- Se analiza mediante la simulación de las ecuaciones de Reynolds de lubricación por FDM (método de diferencias finitas), la distribución de presiones, las fugas, la fuerza y los pares entre el barril y la placa de cierre. La fuerza total y los pares de torsión sobre el barril, se evalúan partiendo de la presión simulada, mostrando que los pares dinámicos que existen sobre el eje XX son mucho menores que los pares actuantes sobre el eje YY. . Pistón cilindro - Se ha investigado el comportamiento del pistón mediante la modificación del número de ranuras y su posición, la distribución de la presión en el intersticio pistón-cilindro, la fuerza sobre el pistón, las fugas y el par de torsión que actúa sobre el pistón se han analizado. También las zonas donde la cavitación es probable que aparezca se han presentado, se discute la forma de prevenir la aparición de cavitación a través del uso de ranuras. La ecuación de lubricación de Reynolds se ha modelizado en el intersticio pistón-cilindro mediante el uso de volúmenes finitos, la excentricidad y el movimiento relativo pistón-cilindro se han considerado. Diferentes configuraciones de ranuras han sido evaluadas con el fin de encontrar mínimas fugas, máximo par y mínima aparición de cavitación. Se especifican instrucciones de diseño para optimizar el comportamiento del pistón. Modelo dinámico de la bomba.- Se ha presentado un amplio conjunto de ecuaciones explícitas para cada parte con movimiento relativo de la bomba de pistones. Todas las ecuaciones se han validado mediante un análisis numérico y en su caso experimental. Las ecuaciones han sido combinadas para estudiar de forma dinámica las perturbaciones de presión y el caudal de fugas. El efecto de la pulsación de caudal cuando se modifica el diseño de la bomba también es presentado. En esta tesis, un modelo de simulación basado en ecuaciones analíticas se ha desarrollado, modelo que produce resultados muy rápidamente y aclara con mucha precisión el efecto de las fugas a través de los diferentes intersticios de la bomba.

    In the field of Fluid Power, piston pumps possess the most sophisticated designs, in fact, pistons pumps are the only ones capable of working at high pressures, besides possessing the best performance (efficiency) of the entire group of existing pumps. However, it is noted that all the designs of piston pumps, are mostly based on the experience of the designers, thus there exist no mathematical tools for optimizing the design of the different parts of the pumps. On the other hand, there are now companies like Oilgear Towler, who inserted slots (grooves) in the slippers and in the pistons, (two major parts of these pumps) but there is no scientific study to analyze its advantages or disadvantages. There is therefore a need to understand mathematically to study the advantages and disadvantages due to the presence of the groove on the surface of different pump parts. There are four sliding surfaces in the piston pump, Slipper-swash plate gap, Barrel-valve plate gap, Piston-barrel chamber gap and Spherical bearing, where lubrication exists and leakages through these channels occur. In this project, our aim is to analyze each of these different sliding surfaces separately to understand its design constrains and the effect of the design parameters on the pump behavior. After having a better understanding of all the different parts of the piston pump, the aim is to model the dynamic behavior of pressure and flow at the outlet of the pump. Slipper plate gap - To understand static and dynamic characteristics of a piston pump slipper with a groove. Three dimensional Navier Stokes equations in cylindrical coordinates have been applied to the slipper/plate gap, including the groove. The results presented in this thesis include, pressure distribution, leakage, force and torque variations when groove dimensions and position are being modified, the effect of slipper tangential velocity and turning speed are also considered. Design instructions to optimize slipper/groove performance are also given. Barrel-valve plate gap - Present thesis, analyses the pressure distribution, leakage, force and torque between the barrel and the port plate of an axial piston pump by simulating Reynolds equations of lubrication by FDM (finite difference method). The overall mean force and torques over the barrel are evaluated from simulated pressure and it shows that the torque over the XX axis is much smaller than the torque over the YY axis. A detailed dynamic analysis is then studied by using the temporal torque calculated by Bergada. Piston-barrel chamber gap - It is being investigated the piston performance by modifying the number of grooves and their position, pressure distribution in the clearance piston-cylinder, leakage force and torque acting over the piston will be discussed, also the locations where cavitation is likely to appear will be presented, discussing how to prevent cavitation from appearing via using grooves. A finite volume based Reynolds equation model has been formulated for the piston-cylinder clearance which considers the piston eccentricity and the relative tangential movement between piston and barrel. Different configurations of the grooves have been evaluated in search of finding minimum leakage, minimum appearance of cavitation and maximum restoring torque. Design instructions to optimize the piston behavior are also given. Full pump Model - An extensive set of explicit equations for every pump gap will be presented. All of the equations will be checked via performing a numerical analysis of the specified pump clearance, the equations will then be combined to study dynamically pressure ripple and leakages. The effect on the flow ripple when modifying the pump design will also be presented. Therefore in present thesis, a simulation model based on analytical equations has been developed which produce very fast results and clarify very precisely the effect of different leakages happened through the pump clearances.

  • Premi Extraordinari de doctorat 2010 corresponents al curs 2007/2008

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Award or recognition

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  • Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Ávila, Matias
    International journal of numerical methods for heat and fluid flow
    Date of publication: 2010
    Journal article

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  • Mixed stabilized finite element methods in nonlinear solid mechanics: part II: strain localization

     Cervera Ruiz, Miguel; Chiumenti, Michele; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-08
    Journal article

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  • Mixed stabilized finite element methods in nonlinear solid mechanics: part I: formulation

     Cervera Ruiz, Miguel; Chiumenti, Michele; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-08-01
    Journal article

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  • Long-term stability estimates and existence of a global attractor in a finite element approximation of the navier-stokes equations with numerical subgrid scale modeling

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Gutierrez Santacreu, Vicente
    SIAM journal on numerical analysis
    Date of publication: 2010
    Journal article

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  • Stabilized continuous and discontinuous Galerkin techniques for Darcy flow

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-05-15
    Journal article

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  • Finite element dynamical sub-grid scale approximation of low mach number flow equations

     Ávila, Matias; Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Argentinean Congress on Computacional Mechanics - South American Congress on Computacional Mechanics
    Presentation of work at congresses

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    In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier Stokes equations in the small Mach number. In contrast to the commonly used Boussinesq approximation, this model permits to take volumetric deformation into account. Although the former is more general than the later, both systems have similar mathematical structure and their numerical approximation can suffer the same type of instabilities. We propose a stabilized finite element approximation based on the the variational multiscale method, in which a decomposition of the approximating space into a coarse scale resolvable part and a fine scale subgrid part is performed. Modeling the subscale and taking its effect on the coarse scale problem into account, results in a stable formulation. The quality of the final approximation (accuracy, efficiency) depends on the particular model. The distinctive features of our approach are to consider the subscales as transient and to keep the scale splitting in all the nonlinear terms. The first ingredient permits to obtain an improved time discretization scheme (higher accuracy, better stability, no restrictions on the time step size). The second ingredient permits to prove global conservation properties. It also allows us to approach the problem of dealing with thermal turbulence from a strictly numerical point of view. Numerical tests show that nonlinear and dynamic subscales give more accurate solutions than classical stabilized methods.

  • The fixed-mesh ALE approach for the numerical approximation of flows in moving domains

     Codina Rovira, Ramon; Houzeaux, G; Coppola Owen, Angel H.; Baiges Aznar, Joan
    Journal of computational physics
    Date of publication: 2009-03
    Journal article

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