A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

JOURNAL OF COMPUTATIONAL PHYSICS

卷:227

Article

Pesch, L.¹  van der Vegt, J. J. W.¹ 

[1] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

关键词: discontinuous Galerkin finite element methods;    Euler equations;    entropy variables;    pseudo-time integration methods;    general equations of state;    compressible flow;    incompressible flow;   

DOI  :  10.1016/j.jcp.2008.01.046

来源: Elsevier

【 摘 要 】

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free