A Runge-Kutta discontinuous Galerkin solver for 2D Boltzmann model equations: Verification and analysis of computational performance

摘要

The high-order Runge-Kutta discontinuous Galerkin (DG) method is extended to the 2D kinetic model equations describing rarefied gas flows. A DG-type discretization of the equilibrium velocity distributions is formulated for the Bhatnagar-Gross-Krook and ellipsoidal statistical models which enforce a weak conservation of mass, momentum and energy in the collision relaxation term. The RKDG solutions have up to 3rd-order spatial accuracy and up to 4th-order time accuracy. Verification is carried out for a steady 1D Couette flow and a 2D thermal conduction problem by comparison with DSMC and analytical solutions. The computational performance of the RKDG method is compared with a widely used second-order finite volume method.