Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

Céline Baranger (1) , Nicolas Hérouard (2) , Julien Mathiaud (1) , Luc Mieussens (3, 2)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
2 IMB - Institut de Mathématiques de Bordeaux
3 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. Most of our analysis relies on a 1D problem (Couette flow), but we also present some results for a 2D aerodynamical flow.

Mots clés: Discrete velocity model; BGK model; Finite Volume Schemes; Rarefied flow simulation; Transitional regime; Numerical boundary conditions; Discontinuous Galerkin schemes

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Céline Baranger, Nicolas Hérouard, Julien Mathiaud, Luc Mieussens. Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries. Mathematics and Computers in Simulation, 2019, 159, pp.136-153. ⟨10.1016/j.matcom.2018.11.011⟩. ⟨hal-01552756v4⟩