Numerical solution of special ultra-relativistic Euler equations using central upwind scheme
Numerical solution of special ultra-relativistic Euler equations using central upwind scheme
复制标题
使用中心迎风格式数值求解特殊超相对论欧拉方程
DOI：
10.1016/j.rinp.2018.03.052
复制
发表时间：
2018
影响因子：
5.3
通讯作者：
Shamsul Qamar
中科院分区：
文献类型：
--
作者：
T. Ghaffar;M. Yousaf;Shamsul Qamar
本文研究一维和二维特殊超相对论欧拉方程的数值逼近。控制方程为一阶非线性双曲型耦合偏微分方程。这些方程描述了理想的流体流动的颗粒密度，四速度和压力。采用高分辨率的激波捕捉中心迎风格式求解模型方程。为了避免过多的数值扩散，所考虑的计划利用本地传播速度的特定信息。采用Runge-Kutta时间步进法和MUSCL型初始重构，我们获得了该格式的二阶精度。在讨论了模型方程和数值方法后，研究了几个一维和二维试验问题。对于所有的数值测试的情况下，我们提出的计划表现出非常好的协议，即使在高度相对论性的2D测试问题的情况下，通过完善的算法所获得的结果。为了验证和比较，交错中心格式和动能通量矢量分裂（KFVS）方法也被应用到同一模式。数值结果表明了中心迎风格式的有效性和鲁棒性。
This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.