Marti, J.; Ortega, E.; Idelsohn, Sergio R. International journal of numerical methods for heat and fluid flow Vol. 27, num. 8, p. 1748-1764 DOI: 10.1108/HFF-06-2016-0219 Data de publicació: 2017-07 Article en revista
The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities. Design/methodology/approach - The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the "cut" elements, a contour integral must be added. These contour integrals named here the "inter-elemental heat fluxes" are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account. Findings - It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE). Originality/value - It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.
The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities. Design/methodology/approach - The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the
Bayona, C.; Baiges, J.; Codina, R. International journal of numerical methods for heat and fluid flow Vol. 26, num. 3-4, p. 1240-1271 DOI: 10.1108/HFF-11-2015-0483 Data de publicació: 2016-03 Article en revista
Purpose - The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.
Design/methodology/approach - The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.
Findings - Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.
Originality/value - A complete investigation of the stabilized formulation of the compressible problem is addressed.
Ávila, M.; Codina, R.; Principe, J. International journal of numerical methods for heat and fluid flow Vol. 25, num. 6, p. 1361-1384 DOI: 10.1108/HFF-07-2014-0238 Data de publicació: 2015 Article en revista
The purpose of this paper is to present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative heat transfer. For high-temperature flows this coupling can have strong effects on the temperature and velocity fields. The basic numerical formulation has been proposed in previous works. It is based on the variational multiscale (VMS) concept in which the unknowns of the problem are divided into resolved and subgrid parts which are modeled to consider their effect into the former. The aim of the present paper is to extend this modeling to the case in which the low Mach number equations are coupled with radiation, also introducing the concept of subgrid scales for the radiation equations. As in the non-radiative case, an important improvement in the accuracy of the numerical scheme is observed when the nonlinear effects of the subgrid scales are taken into account. Besides it is possible to show global conservation of thermal energy. The original contribution of the work is the proposal of keeping the VMS splitting into the nonlinear coupling between the low Mach number and the radiative transport equations, its numerical evaluation and the description of its properties.
Codina, R.; Principe, J.; Ávila, M. International journal of numerical methods for heat and fluid flow Vol. 20, num. 5, p. 492-516 DOI: 10.1108/09615531011048213 Data de publicació: 2010 Article en revista
The purpose of this paper is to describe a variational multiscale finite element approximation for the incompressible Navier-Stokes equations using the Boussinesq approximation to model thermal coupling.
The main feature of the formulation, in contrast to other stabilized methods, is that the subscales are considered as transient and orthogonal to the finite element space. These subscales are solution of a differential equation in time that needs to be integrated. Likewise, the effect of the subscales is kept, both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation.
This strategy allows the approaching of the problem of dealing with thermal turbulence from a strictly numerical point of view and discussion important issues, such as the relationship between the turbulent mechanical dissipation and the turbulent thermal dissipation.
The purpose of this paper is to describe a finite element formulation to approximate thermally coupled flows using both the Boussinesq and the low Mach number models with particular emphasis on the numerical implementation of the algorithm developed.
The formulation, that allows us to consider convection dominated problems using equal order interpolation for all the valuables of the problem, is based on the subgrid scale concept. The full Newton linearization strategy gives rise to monolithic treatment of the coupling of variables whereas some fixed point schemes permit the segregated treatment of velocity-pressure and temperature. A relaxation scheme based on the Armijo rule has also been developed.
A full Newtown linearization turns out to be very efficient for steady-state problems and very robust when it is combined with a line search strategy. A segregated treatment of velocity-pressure and temperature happens to be more appropriate for transient problems.
A fractional step scheme, splitting also momentum and continuity equations, could be further analysed.
The results presented in the paper are useful to decide the solution strategy for a given problem.
The numerical implementation of a stabilized finite element approximation of thermally coupled flows is described. The implementation algorithm is developed considering several possibilities for the solution of the discrete nonlinear problem.
To develop a numerical methodology to simulate the lost foam casting (LFC), including the gas back-pressure effects.
Back-pressure effects are due to the interactions of many physical processes. The strategy proposed herein tries to model all these processes within a simple formula. The main characteristic of the model consists of assuming that the back-pressure is a known function of the external parameters (coating, temperature, gravity, etc.) that affects directly the heat transfer coefficient from the metal to the foam. The general framework of the simulation is a finite element model based on an arbitrary Lagrangian Eulerian (ALE) approach and the use of level set function to capture the metal front advance.
After experimental tunings, the model provides a way to include the back-pressure effects in a simple way.
The method is not completely predictive in the sense that a priori tuning is necessary to calibrate the model.
Provides more realistic results than classical models.
The paper proposes a theoretical framework of a finite element method for the simulation of LFC process. The method uses an ALE method on a fixed mesh and a level-set function to capture metal front advance. It proposes an original formula for the heat transfer coefficient that enables one to include back-pressure effects.
Codina, R.; Morton, C.; Oñate, E.; Soto, O. International journal of numerical methods for heat and fluid flow Vol. 10, num. 6, p. 616-633 DOI: 10.1108/09615530010347196 Data de publicació: 2000-01 Article en revista
Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.
Codina, R.; Schäfer, U.; Oñate, E. International journal of numerical methods for heat and fluid flow Vol. 4, num. 4, p. 291-310 DOI: 10.1108/EUM0000000004108 Data de publicació: 1994-08 Article en revista
In this paper we consider several aspects related to the application of the pseudo-concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div-stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection-dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two-dimensional test problem showing the ability of the method to capture complicated flow patterns.