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Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations

Numerical Analysis 2017-09-13 v1

Abstract

This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook) schemes in the framework of finite volume method for the ultra-relativistic flows. Different from the existing kinetic flux-vector splitting (KFVS) or BGK-type schemes for the ultra-relativistic Euler equations, the present genuine BGK schemes are derived from the analytical solution of the Anderson-Witting model, which is given for the first time and includes the "genuine" particle collisions in the gas transport process. The BGK schemes for the ultra-relativistic viscous flows are also developed and two examples of ultra-relativistic viscous flow are designed. Several 1D and 2D numerical experiments are conducted to demonstrate that the proposed BGK schemes not only are accurate and stable in simulating ultra-relativistic inviscid and viscous flows, but also have higher resolution at the contact discontinuity than the KFVS or BGK-type schemes.

Keywords

Cite

@article{arxiv.1704.08501,
  title  = {Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations},
  author = {Yaping Chen and Yangyu Kuang and Huazhong Tang},
  journal= {arXiv preprint arXiv:1704.08501},
  year   = {2017}
}

Comments

41 pages, 13 figures