Performance of DG methods based on different variables for low Mach number flows

Nicolas Chauchat (1) , Roland Becker (2) , Éric Schall (1)

1 SIAME - Laboratoire des Sciences de l'Ingénieur Appliquées à la Mécanique et au génie Electrique
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Based on its good theoretical properties, the use of entropy variables is an excellent choice for computing compressible flows at low Mach number. In this paper, we discuss the use of entropy variables in a discontinuous Galerkin discretization of the compressible Euler equations and generalize the numerical flux proposed by Barth to physical and conservative variables. Next, we compare the DG0 discretization based on the entropy variables with several other DG0 discretizations, and also with a standard finite volume method. Comparisons of DG1 discretization with the different sets of variables give hope in an all-Mach number solver.

Keywords: Discontinuous Galerkin finite elements method (DGFEM); Euler equations; Entropy variables; Primitive variables; Incompressible limit; Low Mach number

Domains: Fluid mechanics [physics.class-ph]

Nicolas Chauchat, Roland Becker, Éric Schall. Performance of DG methods based on different variables for low Mach number flows. Communications in Nonlinear Science and Numerical Simulation, 2020, ⟨10.1016/j.cnsns.2020.105580⟩. ⟨hal-03009529v2⟩