Three-Dimensional Discontinuous Galerkin Method for the Second-Order Boltzmann-Curtiss Constitutive Model in Continuum-Rarefied Gas Flows

Abstract

A multi-dimensional mixed-type discontinuous Galerkin (DG) method for the second-order Boltzmann-Curtiss constitutive model is presented for continuum-rarefied gas flow problems. An explicit modal DG scheme on unstructured triangular/tetrahedral meshes is adopted for solving the conservation laws in conjunction with the second-order constitutive relations arising from the high degree of thermal non-equilibrium. The performance of the new DG scheme is assessed by solving several test cases such as the subsonic/supersonic/hypersonic gas flows past 2D cylinder, 3D sphere, and 3D flat plate in continuum-rarefied regimes. Finally, multi-dimensional velocity slip models are studied within the framework of DG numerical method.