A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

Abstract

A novel and simple solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number is developed in this work. The present solver combines good features of gas kinetic flux solver (GKFS), discrete velocity method (DVM) and the moment method. Like the GKFS, in the present solver, the macroscopic governing equations are discretized by finite volume method and the numerical fluxes at cell interfaces are evaluated by the local solution of Boltzmann equation. To get the local solution of Boltzmann equation, the initial distribution function is reconstructed with the help of Grad's distribution function, which is inspired from the moment method. For the high order moments in Grad's distribution function, they are computed directly by the moments of distribution function, which is inspired from DVM. In principle, the present solver only needs to discretize the physical space and solves the governing equations resulted from conservation laws of mass, momentum and energy. Thus, its governing equations are much simpler than those of the moment method. To validate the proposed solver, some test examples covering continuum regime and rarefied regime are simulated. Numerical results showed that the present solver can give accurate prediction in the continuum regime and reasonable results as the traditional moment method in the rarefied regime at moderate Knudsen number.