Abstract
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.
| Original language | English |
|---|---|
| Article number | 111195 |
| Journal | Journal of Computational Physics |
| Volume | 460 |
| DOIs | |
| State | Published - 1 Jul 2022 |
Keywords
- Diffusion
- Finite-difference
- h-elliptic property
- High-frequency damping
- Odd-even decoupling
- Viscous
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics