Gas-kinetic scheme for the Euler equations with heat transfer

This paper presents a new gas-kinetic scheme for the numerical solutions of the Euler equations with heat transfer. In the current scheme, the convection and source terms are solved simultaneously for the dynamical evaluation of the gas distribution function around a cell interface, from which the time-dependent numerical fluxes are obtained. In contrast to the Godunov-type schemes, in the gas-kinetic approach the source term can be modeled and included consistently in the gas evolution process. Numerical test cases validate the current method. This scheme can be also generalized to other hyperbolic conservation laws with source terms, e.g., the shallow water equations, if the analogous Bhatnagar-Gross-Krook model can be obtained.