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

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 o...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Baranger, Céline, Hérouard, Nicolas, Mathiaud, Julien, Mieussens, Luc
Format: Article
Language:English
Subjects:
Boundary conditions
Computer simulation
Couette flow
Finite volume method
Galerkin method
Rarefied gas dynamics
Rarefied gases
Two dimensional flow
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2003.05677