A Well-Balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field (Advances in Applied Mathematics and Mechanics, 2010)
In this paper, a well-balanced kinetic scheme for the gas dynamicequations under gravitational field is developed. In order toconstruct such a scheme, the physical process of particles transportthrough a potential barrier at a cell interface is considered, wherethe amount of particle penetration and reflection is evaluatedaccording to the incident particle velocity. This work extends theapproach of Perthame and Simeoni for the shallow water equations[Calcolo, 38 (2001), pp. 201-231] to the Euler equations undergravitational field. For an isolated system, this scheme is probablythe only well-balanced method which can precisely preserve anisothermal steady state solution under time-independentgravitational potential. A few numerical examples are used tovalidate the above approach.