2022/04/01 by Chamarthi, Amareshwara Sainadh, Bokor, Sean, Frankel, Steven H. · 1 citation
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2204.00393
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.