A robust HLLC-type Riemann solver for strong shock
A robust HLLC-type Riemann solver for strong shock
复制标题
强大的 HLLC 型黎曼求解器，可应对强冲击
DOI：
10.1016/j.jcp.2016.01.001
复制
发表时间：
2016-03
影响因子：
4.1
通讯作者：
Guangwei Yuan
中科院分区：
文献类型：
--
作者：
Zhijun Shen;Wei Yan;Guangwei Yuan
众所周知，对于欧拉方程，能够准确捕获接触不连续性的数值格式通常会遭受一些灾难性的红宝石现象，而一些耗散较大的格式，例如HLL格式，则不会受到这种冲击不稳定的影响。将耗散通量与耗散通量较小的混合方案结合起来可以解决冲击不稳定性，但也可能导致其他问题，例如选择开关参数的某些任意性或接触界面变得模糊。为了克服这些缺点，本文提出了一种简单而鲁棒的 HLLC 型黎曼求解器，用于无粘性、可压缩气流，该求解器能够保持锐利的接触表面并且不受不稳定的影响。主要工作是通过修改原有HLL和HLLC方法的剪切粘度，构造HLL型黎曼求解器和HLLC型黎曼求解器。在一些典型的波速估计下，这两种新方案都是积极保守的。此外，还完成了所提出方案的线性矩阵稳定性分析，这表明具有剪切粘性的HLLC型求解器是稳定的，而具有涡量波的HLL型求解器是不稳定的。我们的论点和数值实验表明，与剪切波相关的耗散不足可能是导致不稳定的独特原因。
It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.
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影响因子：
5.2
作者：
J. Moschetta
通讯作者：
J. Moschetta
DOI：
10.2514/6.1988-2904
发表时间：
1988-07
期刊：
The Science of the total environment
影响因子：
--
作者：
K. Peery;S. Imlay
通讯作者：
K. Peery;S. Imlay
影响因子：
4.1
作者：
M. Dumbser;J. Moschetta;J. Gressier
通讯作者：
M. Dumbser;J. Moschetta;J. Gressier
影响因子：
1.8
作者：
Yann Chauvat;J. Moschetta;J. Gressier
通讯作者：
Yann Chauvat;J. Moschetta;J. Gressier
影响因子：
4.1
作者：
D. Pullin
通讯作者：
D. Pullin