A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension
A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension
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DOI：
10.1016/j.jcp.2015.11.017
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
Hua Shen;C. Wen
中科院分区：
文献类型：
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作者：
Hua Shen;C. Wen
Shen等人（2015）[15]提出的特征时空守恒元和解元（CE/SE）格式直接扩展到严格遵循时空守恒定律的二维矩形网格上的多维格式。发展了求解标量守恒律方程和含激波的可压缩欧拉方程的格式。它们准确且稳健，CFL范围从0到接近1。在欧拉解算器中，以常用的Harten、Lax和货车Leer（HLL）Riemann解算器、接触不连续恢复HLLC Riemann解算器和Roe Riemann解算器为例，计算了迎风通量。当采用标准的网格对齐的黎曼解算器，carbuncle现象显着抑制时，与传统的迎风格式相比。如果采用旋转黎曼解算器，则得到了几乎无毛刺的结果。数值算例表明，二维特征CE/SE格式可以很好地同时捕捉激波和复杂流场结构的细节。
The characteristic space–time conservation element and solution element (CE/SE) schemes proposed by Shen et al. (2015) [15] are straightforward extended to multidimensional schemes on 2D rectangular meshes which strictly follow the space–time conservation law. The schemes for solving both scalar conservation laws and compressible Euler equations with shock waves are developed. They are accurate and robust with CFL widely ranging from 0 to nearly 1. In Euler solvers, the frequently-used Harten, Lax and van Leer (HLL) Riemann solver, contact discontinuity restoring HLLC Riemann solver and Roe Riemann solver are employed to calculate the upwind fluxes as examples. When standard grid-aligned Riemann solvers are employed, the carbuncle phenomena are significantly suppressed when comparing with conventional upwind schemes. If rotated Riemann solvers are employed, nearly carbuncle-free results are obtained. Several well understood numerical examples are carried out to demonstrate that the 2D characteristic CE/SE schemes can simultaneously capture shocks and details of complex flow structures very well.