Time-independent gravitational fields in the BGK scheme for hydrodynamics

We incorporate a time-independent grav- itational eld 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 dissipa- tive terms. We perform numerical experiments in both 1D Cartesian geometries and axisymmetric cylindrical coordinates.