A Stable Runge-Kutta Discontinuous Galerkin Solver for Hypersonic Rarefied Gaseous Flows.

A stable high-order discontinuous Galerkin scheme which strictly preserves the positivity of the solution is designed to solve the Boltzmann kinetic model equations. The stability is kept by the accuracy of the velocity discretization, the conservation of the collision terms and a limiter. By requiring the time step smaller than the local mean collision time and forcing positive values of velocity distributions on certain points, the limiter can preserve the positivity of the solutions of the cell average velocity distributions. Verification is performed with a normal shock wave at Mach number of 2.05 and a supersonic flow about a 2D cylinder at Mach number of 6.0. [ABSTRACT FROM AUTHOR]