A three-dimensional modal discontinuous Galerkin method for the second-order Boltzmann-Curtiss-based constitutive model of rarefied and microscale gas flows

Abstract

A three-dimensional mixed modal discontinuous Galerkin (DG) method based on tetrahedral meshes was developed for simulating all flow regimes from subsonic to hypersonic rarefied and microscale gas flows within a single framework. The mixed modal DG scheme was used for solving conservation laws in conjunction with the second-order Boltzmann-Curtiss-based constitutive model of diatomic and polyatomic gases in strong thermal nonequilibrium. A decomposition algorithm based on the compression-expansion and velocity shear sub-problems was presented for solving the multi-dimensional second-order constitutive model. The Langmuir and Maxwell-Smoluchowski velocity-slip and temperature-jump boundary conditions were also implemented into the DG framework. To assess the ability of the new computational model to capture correct physical phenomena, we applied the new model to various gas flows in a wide range of continuum-rarefied and microscale regimes. The computational results in the rarefied and microscale flow regimes showed that the second-order constitutive model yielded solutions that were in better agreement with the direct simulation Monte Carlo and experimental data than the first-order constitutive model.