Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 8, Pages 3781-3803Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2007.11.032
Keywords
Boltzmann equation; BGK equation; compressible Navier-Stokes equations; Chapman-Enskog expansion; asymptotic preserving schemes; micro-macro decomposition
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In this paper, we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier-Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of the Boltzmann (or BGK) equation that couples a kinetic equation with macroscopic ones. This new formulation is then discretized with a semi-implicit time scheme combined with a staggered grid space discretization. Finally, several numerical tests are presented in order to illustrate the efficiency of our approach. Incidentally, we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible Navier-Stokes asymptotics in the case of the simplified BGK model. Up to our knowledge, this property is not known for general collision operators. (C) 2007 Elsevier Inc. All rights reserved.
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