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

Journal Article · Sat May 10 04:00:00 EDT 2008 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2008.01.046· OSTI ID:21159384

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.

• OSTI ID: 21159384
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 11 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPRESSIBLE FLOW
ENTROPY
EQUATIONS OF STATE
FINITE ELEMENT METHOD
FLUID MECHANICS
GALERKIN-PETROV METHOD
GASES
INCOMPRESSIBLE FLOW
NONLINEAR PROBLEMS
THERMODYNAMICS