The wall-jetting effect in Mach reflection: Navier–Stokes simulations

Abstract

The wall-jetting effect in Mach reflections in viscous pseudo-steady flows (as obtained in shock tubes) is investigated numerically. The W-modification of Godunov's scheme has been modified to solve the Navier–Stokes equations using a splitting into physical processes. The viscous terms are approximated using an explicit scheme with central differences in space and a two-step Runge–Kutta method in time. Two analytical models are considered. The first is a self-similar viscous flow model in which we consider a flow field with characteristic size $L$, and assume that as the characteristic size grows from 0 to $L$, the viscosity of the gas ahead of the shock wave varies from 0 to $\mu_{0}$. Consequently, the flow can be made self-similar by using the parameter $\textit{Re}\,{=}\,\rho_{0}a_{0}L/\mu_{0}$. The second is a real non-stationary viscous flow, in which the molecular viscosity during the growth of a characteristic size from 0 to $L$ remains constant and is equal $\mu_{0}$. As a result the viscous effects are only partially accounted for in the self-similar viscous flow model in comparison to a real non-stationary viscous flow model, since they are smaller in the former case. The present investigation complements our previous investigation of the wall-jetting effect in Mach reflection in inviscid pseudo-steady flows (Henderson et al. 2003).