论文标题
特殊相对论流体动力学的二阶精确BGK方案与状态的同步方程
Second-order accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state
论文作者
论文摘要
本文将超相关流量模拟[5]的二阶精确BGK有限体积方案扩展到具有状态同步方程的1D和2D特殊相对论流体动力学。结果表明，由于瞬间积分（三个积分），因此这种2D方案非常耗时，因此它们不再实用。鉴于此，通过在细胞界面的近似非平衡分布中删除BGK方案的近似非平衡分布，而不会损失准确性，则可以通过删除一些术语来提出简化的BGK（SBGK）方案。它们是实际的，因为近似分布的矩积分可以通过某些坐标变换将其简化为单个积分。还讨论了冲击波，稀疏波和接触不连续性之间的左右与右态之间的关系，因此可以得出1D黎曼问题的精确解决方案，并用于数值比较。进行了几项数值实验，以证明所提出的气体运动方案是准确稳定的。 SBGK方案与BGK方案在一个维度上的比较表明，前者在准确性和分辨率方面的表现几乎与后者相同，但效率要高得多。
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 efficiency.
