Astron. Astrophys. Suppl. Ser. 139, 199-217

Time-independent gravitational fields in the BGK scheme for hydrodynamics

A. Slyz¹² - K.H. Prendergast¹

Send offprint request: slyz@mpia-hd.mpg.de

1 - Columbia University, 10027 New York, U.S.A.
2 - Max-Planck Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

Received March 30; accepted April 21, 1999

Abstract:

We incorporate a time-independent gravitational field into the BGK scheme for numerical hydrodynamics. In the BGK scheme the gas evolves via an approximation to the collisional Boltzmann equation, namely the Bhatnagar-Gross-Krook (BGK) equation. Time-dependent hydrodynamical fluxes are computed from local solutions of the BGK equation. By accounting for particle collisions, the fundamental mechanism for generating dissipation in gas flow, a scheme based on the BGK equation gives solutions to the Navier-Stokes equations: the fluxes carry both advective and dissipative terms. We perform numerical experiments in both 1D Cartesian geometries and axisymmetric cylindrical coordinates.

Key words: hydrodynamics -- methods: numerical -- shock waves -- gravitation