论文标题
关于高阶保守有限差异方案中高频阻尼对于粘性通量的重要性
On the Importance of High-Frequency Damping in High-Order Conservative Finite-Difference Schemes for Viscous Fluxes
论文作者
论文摘要
本文讨论了在高阶保守性有限差异方程中高频阻尼对于Navier-Stokes方程中粘性术语的重要性。研究在高分辨率粘性冲击管模拟中遇到的非线性不稳定时，我们发现对粘性方案的修改而不是无粘性方案可以解决围绕冲击的虚假振荡的问题。该修改引入了一个负责高频阻尼的术语，该术语在保守的高阶粘性方案中缺少。阻尼的重要性是针对非结构化网格设计的方案而闻名的。但是，在非常高级的差异方案中，尤其是在保守差异方案中，它尚未得到很好的认可。在这里，我们讨论了如何在保守计划中很容易错过它，以及如何通过适当设计的阻尼术语来改善此类方案。
This paper discusses the importance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Investigating nonlinear instability encountered in a high-resolution viscous shock-tube simulation, we have discovered that a modification to the viscous scheme rather than the inviscid scheme resolves a problem with spurious oscillations around shocks. The modification introduces a term responsible for high-frequency damping that is missing in a conservative high-order viscous scheme. The importance of damping has been known for schemes designed for unstructured grids. However, it has not been recognized well in very high-order difference schemes, especially in conservative difference schemes. Here, we discuss how it is easily missed in a conservative scheme and how to improve such schemes by a suitably designed damping term.
