Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities
Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities
复制标题
防止具有不连续性的可压缩流的基于通量分裂的有限差分法中的数值振荡
DOI：
10.1016/j.jcp.2015.07.049
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发表时间：
2015-11
影响因子：
4.1
通讯作者：
Baolin Tian
中科院分区：
文献类型：
--
作者：
Yousheng Zhang;Xinliang Li;Li Li;Baolin Tian
在模拟具有接触间断或材料界面的可压缩流动时，逐点通量矢量分裂（FVS）或对流项的分量非线性差分离散会引起数值压力和速度振荡。目前的分析表明，这种振荡是由于FVS中特征值逐点分裂的不相容性以及多物质流的质量、动量、能量甚至流体成分方程之间分量非线性差分离散的不一致性造成的。提出了两个实用的原则，以防止这些振荡：（i）对流通量必须分裂的全球FVS，如全球Lax-Friedrichs FVS，和（ii）必须保证不同的方程之间的一致离散。然而，后者是不兼容的组件明智的非线性差分离散。因此，一个一致的离散方法，只使用一组公共的权重，提出了非线性加权本质无振荡（韦诺）格式。一个可能的程序，以确定共同的权重，提供了良好的结果。上述分析和方法适用于两个单一的（例如，接触不连续性）和多材料（例如，材料界面）不连续性。然而，对于后者，附加的流体成分方程应分裂和离散一致的兼容性与其他方程。数值试验包括几个接触不连续性和多物质流证实了所提出的方法的有效性，鲁棒性和低计算成本。
In simulating compressible flows with contact discontinuities or material interfaces, numerical pressure and velocity oscillations can be induced by point-wise flux vector splitting (FVS) or component-wise nonlinear difference discretization of convection terms. The current analysis showed that the oscillations are due to the incompatibility of the point-wise splitting of eigenvalues in FVS and the inconsistency of component-wise nonlinear difference discretization among equations of mass, momentum, energy, and even fluid composition for multi-material flows. Two practical principles are proposed to prevent these oscillations: (i) convective fluxes must be split by a global FVS, such as the global Lax–Friedrichs FVS, and (ii) consistent discretization between different equations must be guaranteed. The latter, however, is not compatible with component-wise nonlinear difference discretization. Therefore, a consistent discretization method that uses only one set of common weights is proposed for nonlinear weighted essentially non-oscillatory (WENO) schemes. One possible procedure to determine the common weights is presented that provided good results. The analysis and methods stated above are appropriate for both single- (e.g., contact discontinuity) and multi-material (e.g., material interface) discontinuities. For the latter, however, the additional fluid composition equation should be split and discretized consistently for compatibility with the other equations. Numerical tests including several contact discontinuities and multi-material flows confirmed the effectiveness, robustness, and low computation cost of the proposed method.
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影响因子：
3.5
作者：
Xinliang Li;Yanwen Ma;Dexun Fu;Xian Liang
通讯作者：
Xian Liang
影响因子：
1
作者：
V. Elling
通讯作者：
V. Elling
影响因子：
4.1
作者：
STEGER, JL;WARMING, RF
通讯作者：
WARMING, RF
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
影响因子：
4.1
作者：
A. Marquina;P. Mulet
通讯作者：
A. Marquina;P. Mulet