A fifth order alternative Compact-WENO finite difference scheme for compressible Euler equations
A fifth order alternative Compact-WENO finite difference scheme for compressible Euler equations
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DOI：
10.1016/j.jcp.2019.108873
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Yufeng Shi;Yan Guo
中科院分区：
文献类型：
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作者：
Yufeng Shi;Yan Guo
在本文中，我们提出了另一种形式的保守五阶有限差分紧致加权本质非振荡（韦诺）格式来求解可压缩欧拉方程。与经典的守恒型有限差分Compact-WENO格式相比，该格式的重构过程是对点值而不是传统的通量函数进行的，因此可以使用HLLC（Harten，Lax and货车Leer）和局部Lax-Friedrichs通量函数计算界面通量。为了保持密度和压力的正性，满足通量限制器的参数化正性与所提出的方案耦合，用于极端条件的问题。给出了包括Titarev-Toro问题、平面Sedov爆炸波问题、Riemann问题、双马赫反射问题、激波绕射问题和Kelvin-Helmholtz不稳定性问题在内的多个测试案例，以证明所提出的紧致格式的高分辨率。
In this paper, we propose an alternative formulation of conservative fifth order finite difference compact Weighted Essentially Non-Oscillatory (WENO) schemes to solve compressible Euler equations. Comparing with the classical conservative finite difference Compact-WENO scheme, its reconstruction procedure is applied to the point values rather than the traditional flux functions, then the HLLC (Harten, Lax and van Leer) and the local Lax-Friedrichs flux functions can be used to compute the interface fluxes in this framework. To maintain positivity of density and pressure, the parametrized positivity satisfying flux limiter is coupled with the proposed scheme for problems with extreme conditions. A number of testing cases including Titarev-Toro problem, the planar Sedov blast-wave problem, Riemann problems, double Mach reflection problem, shock diffraction problem and Kelvin-Helmholtz instability problem are presented to demonstrate the high resolution of the proposed compact scheme.