| Title | Second-order accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state |
| Authors | Chen, Yaping Kuang, Yangyu Tang, Huazhong |
| Affiliation | Northwestern Polytech Univ, Xian Key Lab Sci Computat & Appl Stat, Sch Math & Stat, Xian 710129, Peoples R China Peking Univ, Sch Math Sci, HEDPS, Ctr Appl Phys & Technol, Beijing 100871, Peoples R China Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China |
| Keywords | DISCONTINUOUS GALERKIN METHODS PIECEWISE PARABOLIC METHOD FLUX-SPLITTING METHOD EULERIAN GRP SCHEME KINETIC SCHEMES RIEMANN SOLVER NUMERICAL SCHEME ORDER FLOW MODEL |
| Issue Date | 1-Oct-2021 |
| Publisher | JOURNAL OF COMPUTATIONAL PHYSICS |
| Abstract | This paper extends the second-order accurate BGK finite volume schemes for the ultra-relativistic flow simulations [5] to the 1D and 2D special relativistic hydrodynamics with the Synge equation of state. It is shown that such 2D schemes are very time-consuming due to the moment integrals (triple integrals) so that they are no longer practical. In view of this, the simplified BGK (sBGK) schemes are presented by removing some terms in the approximate nonequilibrium distribution at the cell interface for the BGK scheme without loss of accuracy. They are practical because the moment integrals of the approximate distribution can be reduced to the single integrals by some coordinate transformations. The relations between the left and right states of the shock wave, rarefaction wave, and contact discontinuity are also discussed, so that the exact solution of the 1D Riemann problem could be derived and used for the numerical comparisons. Several numerical experiments are conducted to demonstrate that the proposed gas-kinetic schemes are accurate and stable. A comparison of the sBGK schemes with the BGK scheme in one dimension shows that the former performs almost the same as the latter in terms of the accuracy and resolution, but is much more efficient. (C) 2021 Elsevier Inc. All rights reserved. |
| URI | http://hdl.handle.net/20.500.11897/618821 |
| ISSN | 0021-9991 |
| DOI | 10.1016/j.jcp.2021.110438 |
| Indexed | SCI(E) |
| Appears in Collections: | 数学科学学院 数学及其应用教育部重点实验室 |
