Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 273, Issue -, Pages 160-184Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.05.013
Keywords
Discontinuous Galerkin; Rarefied and microscale gas; Nonlinear coupled constitutive relations
Funding
- National Research Foundation of Korea - Ministry of Education, Science and Technology (Priority Research Centers Program NRF), South Korea [2012-048078]
- National Research Foundation of Korea - Ministry of Education, Science and Technology (Basic Science Research Program), South Korea [2012-R1A2A2A02-046270]
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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. (C) 2014 Elsevier Inc. All rights reserved.
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