A new front tracking scheme for the ultra-relativistic Euler equations
A new front tracking scheme for the ultra-relativistic Euler equations
复制标题
超相对论欧拉方程的一种新的前沿跟踪方案
DOI：
10.1016/j.jcp.2014.06.051
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Matthias Kunik
中科院分区：
文献类型：
--
作者：
M. Abdelrahman;Matthias Kunik
用压力p、无量纲四速度的空间部分u∈ R3和粒子密度n描述理想气体的超相对论欧拉方程。在一维空间中给出了两种求解方程的格式，即波前跟踪格式和锥网格格式。介绍了一种新的波前跟踪技术，它给出了超相对论欧拉方程的弱解。前沿跟踪方法是基于黎曼解的分段常数近似，称为前沿跟踪黎曼解，其中连续稀疏波近似为有限的不连续集合，即所谓的非熵激波。这种方法既可用于分析，也可用于数值计算。本文还导出了一种新的无条件稳定的锥-网格格式，它是基于超相对论欧拉方程的Riemann解。这两种方案进行了比较，通过两个数值例子，其中明确的解决方案是已知的。
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure p, the spatial part u∈ R 3 of the dimensionless four-velocity and the particle density n. Two schemes for these equations are presented in one space dimension, namely a front tracking and a cone-grid scheme. A new front tracking technique for the ultra-relativistic Euler equations is introduced, which gives weak solutions. The front tracking method is based on piecewise constant approximations to Riemann solutions, called front tracking Riemann solutions, where continuous rarefaction waves are approximated by finite collections of discontinuities, so-called non-entropy shocks. This method can be used for analytical as well as for numerical purposes. A new unconditionally stable cone-grid scheme is also derived in this paper, which is based on the Riemann solution for the ultra-relativistic Euler equations. Both schemes are compared by two numerical examples, where explicit solutions are known.