Improved gas kinetic flux solver with locally rescaled Gauss-Hermite quadrature for supersonic continuum and rarefied flows

Abstract

This paper presents an improved Gas Kinetic Flux Solver (GKFS) for simulating supersonic gas flows in both continuum and rarefied regimes. The key of the improvement lies in the use of a rescaled Gauss-Hermite quadrature in particle velocity space, leading to an adaptive velocity strategy in the numerical quadratures for computing the macroscopic variables and the normal flux at each cell interface. This strategy adjusts the quadrature points according to the local flow characteristics, enhancing the solver's ability to handle supersonic continuum and moderately rarefied flows in an efficient way. Numerical simulations of several 1D shock wave test-cases show that fewer quadrature points are need to achieve a good accuracy, comparing with the analytical solution. The improved GKFS has proven capable of simulating 2D oblique shock wave problems, supersonic rarefied flows round the circular cylinder and the NACA0012 airfoil test-cases, with an excellent agreement with the references.