A Well-balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field
In this paper, a well-balanced kinetic scheme for the gas dynamic
equations under gravitational field is developed. In order to
construct such a scheme, the physical process of particles transport
through a potential barrier at a cell interface is considered, where
the amount of particle penetration and reflection is evaluated
according to the incident particle velocity. This work extends the
approach of Perthame and Simeoni for the shallow water equations
[Calcolo, 38 (2001), pp. 201-231] to the Euler equations under
gravitational field. For an isolated system, this scheme is probably
the only well-balanced method which can precisely preserve an
isothermal steady state solution under time-independent
gravitational potential. A few numerical examples are used to
validate the above approach.
