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arXiv · 1704.08501

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

Yaping Chen·Yangyu Kuang·Huazhong Tang
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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.

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Yaping Chen, Yangyu Kuang, Huazhong Tang. 2017-04-27. Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations. https://doi.org/10.1016/j.jcp.2017.08.022

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