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