A triangular discontinuous Galerkin method for non-Newtonian implicit constitutive models of rarefied and microscale gases

作者：Le, N. T. P.; Xiao, H.; Myong, R. S.^*

来源：Journal of Computational Physics, 2014, 273: 160-184.

DOI：10.1016/j.jcp.2014.05.013

• Discontinuous Galerkin
• Rarefied and microscale gas
• Nonlinear coupled constitutive relations

The discontinuous Galerkin (DG) method has been popular as a numerical technique for solving the conservation laws of gas dynamics. In the present study, we develop an explicit modal DG scheme for multi-dimensional conservation laws on unstructured triangular meshes in conjunction with non-Newtonian implicit nonlinear coupled constitutive relations (NCCR). Special attention is given to how to treat the complex non-Newtonian type constitutive relations arising from the high degree of thermal nonequilibrium in multi-dimensional gas flows within the Galerkin framework. The Langmuir velocity slip and temperature jump conditions are also implemented into the two-dimensional DG scheme for high Knudsen number flows. As a canonical scalar case, Newtonian and non-Newtonian convection-diffusion Burgers equations are studied to develop the basic building blocks for the scheme. In order to verify and validate the scheme, we applied the scheme to a stiff problem of the shock wave structure for all Mach numbers and to the two-dimensional hypersonic rarefied and low-speed microscale gas flows past a circular cylinder. The computational results show that the NCCR model yields the solutions in better agreement with the direct simulation Monte Carlo (DSMC) data than the Newtonian linear Navier-Stokes-Fourier (NSF) results in all cases of the problem studied.

• 出版日期2014-9-15