Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities, II
Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities, II
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，II
DOI：
10.1002/fld.4080
复制
发表时间：
2016
影响因子：
1.8
通讯作者：
Tian Baolin
中科院分区：
文献类型：
--
作者：
He Zhiwei;Zhang Yousheng;Li Xinliang;Tian Baolin
提出并分析了基于特征通量分裂的有限差分法在计算具有接触不连续面或材料界面的可压缩流动时存在的问题。分析结果表明：(1)即使采用局部特征分解技术，点方向的通量矢量分裂（FVS）方法，如Steger-Warming FVS或van Leer FVS，也可能引起数值误差。因此，需要使用lax - friedrics型FVS方法。（ii）当材料的等压线为垂直直线时，结合使用局部特征分解和全局lax - friedrich FVS可以避免该材料接触不连续面在加权基本非振荡（WENO）格式下的速度和压力振荡。（iii）对于具有材料界面的问题，如果能够保证真正非线性特征场中的非线性WENO格式是相同的，并且对表示材料界面的分解方程进行适当的离散化，则基于特征的通量分裂的有限差分WENO格式可以实现拟保守方法。版权所有©2015 John Wiley & Sons， Ltd
Problems in the characteristic‐wise flux‐split based finite difference method when compressible flows with contact discontinuities or material interfaces are computed were presented and analyzed. The current analysis showed the following: (i) Even with the local characteristic decomposition technique, numerical errors could be caused by point‐wise flux vector splitting (FVS) methods, such as the Steger–Warming FVS or the van Leer FVS. Therefore, the Lax–Friedrichs type FVS method is required. (ii) If the isobars of a material are vertical lines, the combination of using the local characteristic decomposition and the global Lax–Friedrichs FVS can avoid velocity and pressure oscillations of contact discontinuities in this material for weighted essentially non‐oscillatory (WENO) schemes. (iii) For problems with material interfaces, the quasi‐conservative approach can be realized using characteristic‐wise flux‐split based finite difference WENO schemes if nonlinear WENO schemes in genuinely nonlinear characteristic fields can be guaranteed to be the same and the decomposition equation representing material interfaces is discretized properly. Copyright © 2015 John Wiley & Sons, Ltd.