This paper analyzes a low-dissipation discretization for the resolution of immiscible, incompressible multiphase flow by means of interface-capturing schemes. The discretization is built on a three-dimensional, unstructured finite-volume framework and aims at minimizing the differences in kinetic energy preservation with respect to the continuous governing equations. This property plays a fundamental role in the case of flows presenting significant levels of turbulence. At the same time, the hybrid form of the convective operator proposed in this work incorporates localized low-dispersion characteristics to limit the growth of spurious flow solutions. The low-dissipation discrete framework is presented in detail and, in order to expose the advantages with respect to commonly used methodologies, its conservation properties and accuracy are extensively studied, both theoretically and numerically. Numerical tests are performed by considering a three-dimensional vortex, an exact sinusoidal function, and a spherical drop subjected to surface tension forces in equilibrium and immersed in a swirling velocity field. Finally, the turbulent atomization of a liquid-gas jet is numerically analyzed to further assess the capabilities of the method.
The turbulent flow around a circular cylinder has been investigated at Re=5000Re=5000 using direct numerical simulations. Low frequency behavior, vortex undulation, vortex splitting, vortex dislocations and three dimensional flow within the wake were found to happen at this flow regime. In order to successfully capture the wake three dimensionality, different span-wise lengths were considered. It was found that a length LZ=2pDLZ=2pD was enough to capture this behavior, correctly predicting different aspects of the flow such as drag coefficient, Strouhal number and pressure and velocity distributions when compared to experimental values. Two instability mechanisms were found to coexist in the present case study: a global type instability originating in the shear layer, which shows a characteristic frequency, and a convective type instability that seems to be constantly present in the near wake. Characteristics of both types of instabilities are identified and discussed in detail. As suggested by Norberg, a resonance-type effect takes place in the vortex formation region, as the coexistence of both instability mechanisms result in distorted vortex tubes. However, vortex coherence is never lost within the wake.
In this paper, a three-field finite element stabilized formulation for the incompressible viscoelastic fluid flow problem is tested numerically. Starting from a residual based formulation, a non-residual based one is designed, the benefits of which are highlighted in this work. Both formulations allow one to deal with the convective nature of the problem and to use equal interpolation for the problem unknowns View the MathML sources-u-p (deviatoric stress, velocity and pressure). Additionally, some results from the numerical analysis of the formulation are stated. Numerical examples are presented to show the robustness of the method, which include the classical 4: 1 planar contraction problem and the flow over a confined cylinder case, as well as a two-fluid formulation for the planar jet buckling problem.
In previous works [S. R. Idelsohn, J. Marti, P. Becker, E. Oñate, Analysis of multifluid flows with large time steps using the particle finite element method, International Journal for Numerical Methods in Fluids 75 (9) (2014) 621–644. doi:10.1002/fld.3908. URL http://dx.doi.org/10.1002/fld.3908, Juan M. Gimenez and Leo M. González, An extended validation of the last generation of particle finite element method for free surface flows, J Comput Phys 284 (0) (2015) 186–205. doi:http://dx.doi.org/10.1016/j.jcp.2014.12.025. URL http://www.sciencedirect.com/science/article/pii/S0021999114008420 ], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [S. Idelsohn, N. Nigro, A. Limache, E. Oñate, Large time-step explicit integration method for solving problems with dominant convection, Comp Methods in Appl Mech Eng 217–220 (2012) 168–185.] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy.
Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.
A new single-phase scheme for the numerical simulation of free-surface problems on 3-D unstructured meshes is presented. The flow field is obtained from the discrete solution of the incompressible Navier-Stokes equations, whereas a conservative level-set method is employed to capture fluid interfaces on an Eulerian approach. The scheme is based on a novel treatment of the interface for the deactivation of the light phase, allowing an optimization of the classic two-phase model for the cases in which the influence of the lighter phase is negligible. The deactivation is performed by directly imposing the appropriate pressure at the surface boundary, and, unlike similar approaches, without the need to treat near-interface velocities. The method is validated against various analytical and experimental references, demonstrating its potential on both hexahedral and unstructured meshes. Moreover, it shows higher numerical stability in comparison to two-phase solvers, as well as significant advantages in terms of computational performance.
The computation of flow-induced noise at low Mach numbers usually relies on a two-step hybrid methodolgy. In the first step, an incompressible fluid dynamics simulation (CFD) is performed and an acoustic source term is derived from it. The latter becomes the inhomogeneous term for an acoustic wave equation, which is solved in the second step, often resorting to boundary integral formulations. In the presence of rigid bodies, Curie's acoustic analogy is probably the most extended approach. It has been shown that Curie's boundary dipolar noise contribution does in fact correspond to the diffraction of the quadrupolar aerodynamic noise generated by the flow past the rigid body. In this work, advantage is taken from this fact to propose an alternative computational methodology to get the individual quadrupolar and dipolar contributions to the total acoustic pressure. For any linear acoustic wave operator, the unknown acoustic pressure can be split into its incident and diffracted components and be computed simultaneously to the incompressible flow field, in a single finite element computational run. This circumvents the problem found in Curie's analogy of needing the total pressure at the body's boundary, which includes the acoustic pressure fluctuations. The latter cannot be obtained from an incompressible CFD simulation. The proposed unified strategy could be beneficial for a large variety problems such as those involving noise generated from duct terminations, or those related with the simulation of fricatives in numerical voice production, among many others.
This paper presents a methodology for simulation of two-phase flows with surface tension in the framework of unstructured meshes, which combines volume-of-fluid with level-set methods. While the volume-of-fluid transport relies on a robust and accurate polyhedral library for interface advection, surface tension force is calculated by using a level-set function reconstructed by means of a geometrical procedure. Moreover the solution of the fluid flow equations is performed through the fractional step method, using a finite-volume discretization on a collocated grid arrangement. The numerical method is validated against two- and three-dimensional test cases well established in the literature. Conservation properties of this method are shown to be excellent, while geometrical accuracy remains satisfactory even for the most complex flows.
The turbulent flow around a square cylinder at Reynolds number 22,000 (based on the cylinder diameter and the inflow velocity) is studied by means of direct numerical simulation. An overview of the numerical methods and the methodology used to verify the simulation is presented with special emphasis to determine the proper domain size and time-integration period. Then, the time-averaged flow results and turbulent statistics are discussed together with available experimental data showing a fairly good agreement. Finally, frequency analysis of velocity samples is used to analyze both the Kelvin-Helmholtz vortical structures produced by the flow separation at the leading edge of the cylinder and the Von Karman vortex shedding in the wake region. The former are observed more downstream compared with the experiments suggesting that transition to turbulence may occur later. However, comparison of the turbulent statistics in the near wall region indicates that transition is being well captured.
In this study, parallelization of a Discrete Element Method (DEM) code titled Trubal was carried out based on the CPU-GPU heterogeneous architecture where both two- and three-dimensional cases were assessed. In Trubal, the particle-particle/wall interaction rules are governed by the theoretical contact mechanics which enable the direct use of real physical material properties in the calculation. We reconstructed Trubal in two steps: reconstruction of the static storage structure; essential parallelism on the relative newer version code. Numerical simulations were implemented to present the benefits of this research. Firstly, two simulations of die filling with a moving shoe involving 6000 and 60,000 two-dimensional particles were conducted under (i) NVIDIA Tesla C2050 card together with Intel Core-Duo 2.93 GHz CPU and (ii) NVIDIA Tesla K40c card along with Intel Xeon 3.00 GHz CPU. Average speedups of (i) 4.69 and 12.78 as well as (ii) 6.52 and 18.60 in computational time were obtained, respectively. Then, a simulation of die filling with a stationary shoe containing 20,000 three-dimensional particles was carried out under the same conditions where average speedups of (i) 12.90 and (ii) 19.66 in computational time were obtained, respectively. It is shown that the final version parallel code gave a substantial acceleration on the original Trubal.
In this paper a parallel adaptive mesh refinement (AMR) strategy for large eddy simulations (LES) of turbulent flows is presented. The underlying discretization of the Navier-Stokes equations is based on a finite-volume symmetry-preserving formulation, with the aim of preserving the symmetry properties of the continuous differential operators and ensure both, stability and conservation of kinetic-energy balance. The conservation properties are tested for the meshes resulting from the AMR process, which typically contain transitions between zones with different level of refinement. Our AMR scheme applies a cell-based refinement technique, with a physics-based refinement criteria based on the variational multi-scale (VMS) decomposition theory. The overall AMR process, from the selection of the cells to be refined/coarsened till the pre-processing of the resulting mesh, has been implemented in a parallel code, for which the parallel performance has been attested on an AMD Opteron based supercomputer. Finally, the robustness and accuracy of our methodology is shown on the numerical simulation of the turbulent flow around a square cylinder at Re = 22,000 and the turbulent flow around two side-by-side square cylinders at Re = 21,000.
In this work we present a numerical model for the estimation of atmospheric seeing in observation sites. The particularity of the method is that it is based on a Variational Multiscale turbulence model, its main feature being that the numerical mechanisms which are used to deal with stability issues (convection and the inf–sup condition for incompressible flows) do also take care of the modeling of turbulence. Based on this turbulence model, we develop the expressions for the viscous and thermal dissipations, ¿num¿num and ¿num¿num, which are later used for evaluating the constant of structure of the refraction index View the MathML sourceCn2 following the classical model developed by Tatarski. Numerical examples show the behavior of the proposed numerical scheme when applied to turbulent flow practical cases, which include a convective boundary layer, the flow inside a transfer optics room, and a telescope enclosure.
A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of the approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given output of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations. (C) 2014 Published by Elsevier Ltd.
Objective: In this article we study the approximation to thermal turbulence from a strictly numerical point of view, without the use of any physical model. The main goal is to analyze the behavior of our numerical method in the large eddy simulation (LES) of thermally coupled turbulent flows at low Mach number.; Methods: Our numerical method is a stabilized finite element approximation based on 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 as LES model) depends on the particular subscale 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.; Another important contribution of this work is the extension of the orthogonal subgrid scale method widely tested for incompressible flows to variable density flows, using a density-weighted L-2 product to define the orthogonality of the subscales and the finite element spaces.; Results: Referring to numerical testing, we present numerical results for a laminar testcase validation that shows the dissipative behavior of the different stabilized methods. Then, we present results of the numerical simulation of two turbulent flow problems, the turbulent channel flow with large temperature differences in the wall normal direction at Re-tau = 180, and the turbulent thermally driven cavity with aspect ratio 4. The behavior of the method is evaluated by comparison against results available in the literature obtained using LES and direct numerical simulation (DNS). They are explained based on a careful analysis of the dissipative structure of the method, showing the physical interpretation of the subgrid scale method presented.; conclusion: The material presented here is a clear indication of the potential of the method to model all kinds of turbulent thermally coupled flows. The formulation is the same in laminar and turbulent regimes. (C) 2014 Elsevier Ltd. All rights reserved.
External car aerodynamics study has great importance in overall car efficiency and ride stability, being a key element in successful automotive design. The flow over car geometries shows three dimensional and unsteady turbulent characteristics. Additionally, vortex shedding, flow reattachment and recirculation bubbles are also found around the bluff body. These phenomena greatly influence the lift and drag coefficients, which are fundamental for ride stability and energy efficiency, respectively. The aim of the present study is focused on the assessment of different LES models (e.g. VMS or SIGMA models), as well as to show their capabilities of capturing the large scale turbulent flow structures in car-like bodies using relative coarse grids. In order to achieve these objectives, the flow around two model car geometries, the Ahmed and the Asmo cars, is simulated. These generic bluff bodies reproduce the basic fluid dynamics features of real cars. First, the flow over both geometries is studied and compared against experimental results to validate the numerical results. Then, different LES models are used to study the flow in detail and compare the structures found in both geometries.
Zhang, H.; Tan, Y.; Shu, S.; Niu, X.; Trias, F. X.; Yang, D.; Li, H.; Sheng, Y. Computers and fluids Vol. 94, p. 37-48 DOI: 10.1016/j.compfluid.2014.01.032 Data de publicació: 2014-05-01 Article en revista
Particle collisions play a very important role in determining the fluid-particle multiphase flow, and thus it is crucial to treat the particle-particle interaction using a felicitous method in numerical simulations. A novel combined lattice Boltzmann method (LBM)-immersed boundary method (IBM)-discrete element method (DEM) scheme is presented in this study with its application to model the sedimentation of 2D circular particles in incompressible Newtonian flows. The hydrodynamic model of the incompressible Newtonian flow is based on the Bhatnagar-Gross-Krook LBM, and a momentum exchange-based IBM is adopted to calculate the fluid-solid interaction force. The kinematics and trajectory of the discrete particles are evaluated by DEM, in which the particle-particle interaction rules are governed by theoretical contact mechanics to enable the direct use of real particle properties. This eliminates the need of artificial parameters and also improves the reliability of the numerical results. By using a more accurate and physical description of particle interaction, a 'safe zone' or threshold is also no longer required. Case studies of single particle settling in a cavity, and two particles settling in a channel were carried out, the velocity characteristics of the particle during settling and near the bottom were examined. A numerical example of sedimentation involving 504 particles was finally presented to demonstrate the capability of the combined scheme.
A new geometrical Volume-of-Fluid (VOF) method for capturing interfaces on three-dimensional (3-D) Cartesian and unstructured meshes is introduced. The method reconstructs interfaces as first- and second-order piecewise planar approximations (PLIC), and advects volumes in a single unsplit Lagrangian–Eulerian (LE) geometrical algorithm based on constructing flux polyhedrons by tracing back the Lagrangian trajectories of the cell-vertex velocities. In this way, the situations of overlapping between flux polyhedrons are minimized, consequently, the accuracy in the solution of the advection equation is improved by minimizing the creation of overshoots (volume fractions over one), undershoots (volume fractions below zero) and wisps (fluid in void regions or vice versa). However, if not treated carefully, the use of cell-vertex velocities may result in the construction of flux polyhedrons that contain nonplanar faces and that do not conserve volume. Therefore, this work explains in detail a set of geometric algorithms necessary to overcome these two drawbacks. In addition, the new VOF method is analyzed numerically on 3-D Cartesian and unstructured meshes, first, by reconstructing the interface of spherical geometries and, second, by evaluating the final advection result of a sphere placed in a rotation, shear and deformation field.
The preconditioned conjugate gradient (PCG) is one of the most prominent iterative methods for the solution of sparse linear systems with symmetric and positive definite matrix that arise, for example, in the modeling of incompressible flows. The method relies on a set of basic linear algebra operations which determine the overall performance. Therefore, to achieve improvements in the performance, implementations of these basic operations must be adapted to the changes in the architecture of parallel computing systems. In the last years, one of the strategies to increase the computing power of supercomputers has been the usage of Graphics Processing Units (GPUs) as math co-processors in addition to CPUs. This paper presents a MPI-CUDA implementation of the PCG solver for such hybrid computing systems composed of multiple CPUs and CPUs. Special attention has been paid to the sparse matrix-vector multiplication (SpMV), because most of the execution time of the solver is spent on this operation. The approximate inverse preconditioner, which is used to improve the convergence of the CG solver, is also based on the SpMV operation. An overlapping of data transfer and computations is proposed in order to hide the MPI and the CPU-GPU communications needed to perform parallel SpMVs. This strategy has shown a considerable improvement and, as a result, the hybrid implementation of the PCG solver has demonstrated a significant speedup compared to the CPU-only implementation.
A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, the performance of the FPM flow solver is compared with an equivalent edge-based Finite Element (FEM) implementation. Efficiency issues have discouraged practical application of meshless methods in the past. Thus, a simplification of the basic FPM technique is proposed in order to reduce the performance gap with respect to classical grid-based algorithms. A comparative evaluation of the accuracy, computational cost and parallel performance of the meshless implementation is carried out with the objective to assess the level of maturity of the technique and identify improvements still required to tackle practical applications. The results obtained show accuracy and performance of the core algorithm comparable to a conventional FEM implementation, thus removing a major obstacle for further developments of the FPM.
The Boltzmann transport equation is solved in the context of radiative heat transfer, for an isotropically scattering medium with reflecting boundaries. Under these circumstances, the different ordinates of the angular flux are mutually coupled. We explore here the use of a parallel sweep-based block diagonal preconditioner as a complement of the GMRES solver on the solution of the discretization matrix (which includes all the inter-ordinate couplings). The validity of this approach, when compared to the standard source iteration scheme, is successfully assessed for a significant range of the coupling parameters.
This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off between the mesh refinement during the optimization process and the improvement of the optimized solution. This subject is investigated in the transonic airfoil design optimization using an Adaptive Mesh Refinement (AMR) technique coupled to Multi-Objective Genetic Algorithm (MOGA) and an Euler aerodynamic analysis tool. The methodology is implemented to solve three practical design problems; the first test case considers a reconstruction design optimization that minimizes the pressure error between a predefined pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coefficient (Cl). The solutions obtained with and without adaptive mesh refinement are compared in terms of solution improvement and computational cost. Numerical results clearly show that the use of adaptive mesh refinement can improve the solution accuracy while reducing significant computational cost in both single- and multi-objective design optimizations.
The work is devoted to the development of efficient parallel algorithms for large-scale simulations of incompressible flows on hybrid supercomputers based on massively-parallel accelerators. The governing equations are discretized using a high-order finite-volume scheme for Cartesian staggered meshes with the only restriction that, at least, one direction is periodic. Its “classical” MPI + OpenMP parallel implementation for CPUs was designed to scale till 100,000 CPU cores. The new hybrid algorithm is developed on a base of a multi-level parallel model that exploits several layers of parallelism of a modern hybrid supercomputer. In this model, MPI and OpenMP are used on the first two levels to couple nodes of a supercomputer and to engage its CPU cores. Then, computing accelerators are further used by means of the hardware independent OpenCL computing standard. In this way, the implementation is adapted to a general computing model with central processors and math co-processors. In this paper the work is focused on adapting the basic operations of the algorithm to architectures of Graphics Processing Units (GPU) without considering the multi-GPU communication scheme. Technology of porting the code to OpenCL is described, certain optimization approaches are presented and relevant performance results obtaining up to 80–90 GFLOPS on a GPU accelerator are demonstrated.
Moreover, the experience with different GPU architectures is summarized and a comparison based on the particular application is given for AMD and NVIDIA GPUs as well as for CUDA and OpenCL frameworks.
This paper investigates the capabilities of two subgrid-scale (SGS) models suitable for unstructured grids for predicting the complex flow in transitional separated bubbles. The flow over a NACA 0012 airfoil at Reynolds number Re = 5e4 and angles of attack (AOA) AOA = 5° and 8° is here considered. The SGS models investigated are: the wall-adapting eddy viscosity model within a variational multiscale method (VMS-WALE) and the QR eddy-viscosity model. Both are well suited for large-eddy simulations (LES) in complex geometries with unstructured grids. The models are assessed and compared to the results of direct numerical simulations (DNS) on the basis of first and second order statistics. Based on the good results obtained, specially with the VMS-WALE model, challenging simulations at high Reynolds numbers and various AOA are also performed. It has been found that predictions of the lift and drag coefficients agree reasonably well with experimental data.
Direct numerical simulations of the flow over a sphere have been performed. The computations have been carried out in the sub-critical regime at Re = 3700 and Re = 10,000 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation has been used for simulating the flow. Computations have been carried out on unstructured grids obtained by the constant-step rotation about the axis of a two-dimensional grid. With this discretisation, the Poisson equation has been solved by means of a Fourier diagonalization method. Particular attention has been devoted to investigate the shear-layer instabilities and its influence in the vortical structures, as well as the wake configuration. The main features of the flow including power spectra of a set of selected monitoring probes at different positions have been described and discussed in detail. Detailed information about turbulent statistics have also been provided.
Dadvand, P.; Rossi, R.; Gil, Marisa; Martorell, X.; Cotela, J.; Juanpere, E.; Idelsohn, Sergio R.; Oñate, E. Computers and fluids Vol. 80, num. 1, p. 301-309 DOI: 10.1016/j.compfluid.2012.02.004 Data de publicació: 2013-07-10 Article en revista
Creating a highly parallelizable code is a challenge specially for Distributed Memory Machines (DMMs). Moreover, algorithms and data structures suitable for these platforms can be very different from the ones used in serial code. For this reason, many programmers in the field prefer to start their own code from scratch. However, for an already existing framework supported by a long-time expertise the idea of transformation becomes attractive in order to reuse the effort done during years of development. In this presentation we explain how a relatively complex framework but with modular structure can be prepared for high performance computing with minimum modification. Kratos Multi-Physics  is an open source generic multi-disciplinary platform for solution of coupled problems consist of fluid, structure, thermal and electromagnetic fields. The parallelization of this framework is performed with objective of enforcing the less possible changes to its different solver modules and encapsulate the changes as much as possible in its common kernel. This objective is achieved thanks to the Kratos design and also innovative way of dealing with data transfers for a multi-disciplinary code. This work is completed by the migration of the framework from the 86× architecture to the Marenostrum Supercomputing platform. The migration has been verified by a set of benchmarks which show high scalability, from which we present the Telescope problem in this paper.
Creating a highly parallelizable code is a challenge specially for distributed memory machines (DMMs). Moreover, algorithms and data structures suitable for these platforms can be very different from the ones used in serial code. For this reason, many programmers in the field prefer to start their own code from scratch. However, for an already existing framework supported by a long-time expertise the idea of transformation becomes attractive in order to reuse the effort done during years of development. In this presentation we explain how a relatively complex framework but with modular structure can be prepared for high performance computing with minimum modification. Kratos Multi-Physics  is an open source generic multi-disciplinary platform for solution of coupled problems consist of fluid, structure, thermal and electromagnetic fields. The parallelization of this framework is performed with objective of enforcing the less possible changes to its different solver modules and encapsulate the changes as much as possible in its common kernel. This objective is achieved thanks to the Kratos design and also innovative way of dealing with data transfers for a multi-disciplinary code. This work is completed by the migration of the framework from the x86 architecture to the Marenostrum Supercomputing platform. The migration has been verified by a set of benchmarks which show high scalability, from which we present the Telescope problem in this paper.
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed algorithm is effective both for local adaptive refinement and for the division of all the elements within an existing mesh. We aim to provide sufficient detail to allow the practical implementation of the algorithm, which can be coded with minimal effort provided that a distributed linear algebra library is available. The proposed refinement strategy is composed of three basic components: a global splitting strategy, an elemental splitting procedure and an error estimation technique, which are combined so to guarantee obtaining a conformant refined mesh. A number of benchmark examples show the capabilities of the proposed method. Error is estimated for the incompressible fluid-flow benchmarks using a novel indicator based on the computation of the sub-scale velocity.
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed algorithm is effective both for local adaptive refinement and for the division of all the elements within an existing mesh. We aim to provide sufficient detail to allow the practical implementation of the algorithm, which can be coded with minimal effort provided that a distributed linear algebra library is available. The proposed refinement strategy is composed of three basic components: a global splitting strategy, an elemental splitting procedure and an error estimation technique, which are combined so to guarantee obtaining a conformant refined mesh. A number of benchmark examples show the capabilities of the proposed method. Error is estimated for the incompressible fluid-flow benchmarks
using a novel indicator based on the computation of the sub-scale velocity.
The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance of a portable state-of-the-art FE solver on GPU accelerators. Performance evaluation is done by comparing with an existing highly-optimized OpenMP version of the solver. Code portability is ensured by writing the program using the OpenCL 1.1 specifications, while performance portability is sought through an optimization step performed at the beginning of the calculations to find out the optimal parameter set for the solver. The results show that the new implementation can be several times faster than the OpenMP version.
The rise of GPUs in modern high-performance systems increases the interest in porting
portion of codes to such hardware. The current paper aims to explore the performance
of a portable state-of-the-art FE solver on GPU accelerators. Performance evaluation is
done by comparing with an existing highly-optimized OpenMP version of the solver.
Code portability is ensured by writing the program using the OpenCL 1.1 specifications,
while performance portability is sought through an optimization step performed
at the beginning of the calculations to find out the optimal parameter set for the solver.
The results show that the new implementation can be several times faster than the
Huang , X.; Valero, M.; Egusquiza, E.; Presas, A.; Guardo, A. Computers and fluids Vol. 71, num. January, p. 54-64 DOI: 10.1016/j.compfluid.2012.09.016 Data de publicació: 2013-01-30 Article en revista
This paper investigates the effect of water in the dynamic response of large trash-racks used in hydropower plants. These are large structures that are fully submerged in water and located in the hydraulic circuits to prevent debris and large bodies from entering the turbine. These structures are prone to suffering fatigue damage. Broken bars are rather common, which can produce damage in the turbine and other hydraulic components.
To avoid fatigue problems, the trash-racks must be designed to avoid coincidence between the excitation frequencies of vortex shedding and the natural frequencies of the trash rack. Therefore, it is of paramount importance to know which are the natural frequencies and the associated mode-shapes, so as to avoid fluid–structure coupling (lock-in), which can lead to high vibration levels. Finite element models, including the surrounding mass of water, are used for this study.
The methodology is applied to two existing trash-racks by calculating the modal parameters and using the numerical finite element model. An experimental investigation is also carried out in one of the trash-racks by impacting the underwater grille and measuring the response using submergible accelerometers. Experimental modal analysis is utilized to extract the modal characteristics of the actual trash rack. There is a good agreement between the numerical and the experimental results. With the validated model, the effects of fluid added mass and damping on the dynamic response of both trash-racks are evaluated and discussed in order to extract some common conclusions.
Structural–acoustical model is used in industry to determine natural frequencies of runners and impellers
in hydraulic turbomachinery in the stage of design. In these calculations the fluid domain is considered
with comparable large distances to stationary parts while there are parts of the submerged structure
(runner or impeller) that are extremely close (in relation to its thickness) to a rigid surface (hydraulic
seals). These seals are not considered in the numerical model because it is assumed that structural–
acoustical model is not capable to predict natural frequencies with nearby rigid surfaces. The present
work builds a fluid structure interaction numerical model based on structural–acoustic coupling, checks
the numerical model’s accuracy, and determines its capability to predict natural frequencies reduction
due to nearby rigid surfaces comparing this model against experimental data of submerged cantilever
plates. It is found that the structural–acoustical model can accurately predict the natural frequencies
for submerged structures with nearby rigid surfaces with averaged absolute errors of 2.5%. This is an
interesting result because it suggests that simulation of runners and impellers can be carried out considering
the effect of hydraulic seals, therefore, obtaining natural frequencies that are closer to those found
The main objective of the present paper is the assessment of symmetry-preserving regularization models on unstructured meshes. Three different test cases have been studied: the impinging jet flow, the flow past a circular cylinder and a simplified Ahmed car. The properties of the filters and their performance on general unstructured meshes have also been considered. A detailed analysis considering the Gaussian and the Helmholtz differential filters is presented.
This work is devoted to the development of efficient parallel algorithms for the direct numerical simulation (DNS) of incompressible flows on modern supercomputers. In doing so, a Poisson equation needs to be solved at each time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is the part of the algorithm that is most difficult to parallelize.
The Poisson solver presented here is restricted to problems with one uniform periodic direction. It is a combination of a block preconditioned Conjugate Gradient (PCG) and an FFT diagonalization. The latter
decomposes the original system into a set of mutually independent 2D systems that are solved by means of the PCG algorithm. For the most ill-conditioned systems, that correspond to the lowest Fourier frequencies,
the PCG is replaced by a direct Schur-complement based solver.
The previous version of the Poisson solver was conceived for single-core (also dual-core) processors and therefore, the distributed memory model with message-passing interface (MPI) was used. The irruption of multi-core architectures motivated the use of a two-level hybrid MPI + OpenMP parallelization with the shared memory model on the second level. Advantages and implementation details for the additional
OpenMP parallelization are presented and discussed in this paper. Numerical experiments show that, within its range of efficient scalability, the previous MPI-only parallelization is slightly outperformed
by the MPI + OpenMP approach. But more importantly, the hybrid parallelization has allowed to significantly extend the range of efficient scalability. Here, the solver has been successfully tested up to 12800 CPU cores for meshes with up to 109 grid points. However, estimations based on the presented
results show that this range can be potentially stretched up until 200,000 cores approximately.
Finally, several examples of DNS simulations are briefly presented to illustrate some potential applications of the solver.
Trias, F. X.; Verstappen, R.W.C.P.; Gorobets, A.; Soria, M.; Oliva, A. Computers and fluids Vol. 39, num. 10, p. 1815-1831 DOI: 10.1016/j.compfluid.2010.06.016 Data de publicació: 2010-06-23 Article en revista
Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity
cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present
work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore,
the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4 X 10 8 ≤ Ra ≤ 10 11 shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 10 17. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.
An efficient and accurate numerical scheme is proposed to solve the incompressible Navier–Stokes equations in a bounded cylinder. The scheme is based on a projection method formulated in primitive variables to maintain the incompressibility constraint, with a second-order semi-implicit scheme for the time integration, and a pseudospectral approximation for the space variables. The Chebyshev-collocation method applied in the radial and axial directions, and the Fourier–Galerkin approximation used in the azimuthal direction lead to a sequence of two-dimensional Helmholtz and Poisson equations for every azimuthal coefficient that are solved by a diagonalization technique. Radial expansions are considered in the diameter of the cell in order to avoid clustering about the axis, and the number of points are selected to ensure that r=0 is not a collocation point. A minimal number of regularity conditions are imposed implicitly at the origin by forcing the proper parity of the Fourier expansions in the radial direction. The method has been tested on analytical solutions and compared with other reliable three-dimensional results. The improvements introduced in the treatment of the spatial discretization reduce significantly the difficulty of implementation of the code, and facilitate the use of high resolutions. Different boundary conditions can also be easily implemented.
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.
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
We present in this paper a numerical strategy for the simulation of rotary positive displacement pumps, taking as an example a gear pump. While the two gears of the pump are rotating, the intersection between them changes in time. Therefore, the computational domain should be recomputed in some way at each time step. The strategy used here consists in dividing a cycle into a certain number of time steps and obtaining different computational meshes for each of these time steps. The coupling between two consecutive time steps is achieved by interpolating the flow unknowns in a proper way. This geometrical decomposition enables one to have a plain control over the mesh, particularly in the zones of interest, which are the gap between the gears and the casing, and the engagement and disengagement zones of the gears.
When one wants to simulate flows with moving bodies and when there is no possible way of prescribing simple boundary conditions in any frame of reference, one possibility is the use of domain decomposition methods. The domain decomposition method we present in this work aims at coupling overlapping subdomains in relative motion using a Dirichlet/Neumann coupling. The method is applied to the solution of incompressible and turbulent flows.