Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier–Stokes asymptotics
Langue
en
Article de revue
Ce document a été publié dans
Journal of Computational Physics. 2008, vol. 227, n° 8, p. 3781-3803
Elsevier
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
Boltzmann equation
BGK equation
Compressible Navier–Stokes equations
Chapman–Enskog expansion
Asymptotic preserving schemes
Micro–macro decomposition
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