对称性与激波捕捉中的非物理波动问题

Symmetry and Non-Physical Oscillation in Shock Capturing

众所周知传统的一些激波捕捉格式(如Godunov,Roe格式)仪靠格式本身的耗散无法完全抑制激波下游的振荡。本文从微分方程拥有的内在对称性角度对此问题进行探讨。指出了Lax-wendroff格式数值求解无粘 Burgers方程的问题出现空间振荡与对称破缺之间的内在联系。本文的研究表明:对称破缺可能是在激波附近导致数值解出现三种异常现象的内在机制。

It is known that for some of the traditional shock-capturing schemes, such as the Godunov or Roe type methods, will generate downstream oscillatory wave patterns that cannot be effectively damped by the dissipation of these schemes. The theme of this paper is to understand the formation and behavior at these upstream/downstream patterns from the point views of symmetry inherent in the PDE. Symmetry breaking and the spatial oscillations in finite difference solutions for the inviscid Burgers equation using the Lax-Wendroff scheme are explored. Symmerty breaking may be the inherent cause for the nonphysical oscillations in the vicinity of the shock.