Computational simulations of microscale shock–vortex interaction using a mixed discontinuous Galerkin method

Abstract

This study extensively investigates the physics of microscale shock–vortex interaction of argon gas by solving conservation laws with non-Newtonian constitutive relations. In order to solve the conservation laws and associated implicit type second-order constitutive equations of viscous stress and heat flux numerically, a mixed discontinuous Galerkin (DG) formulation is developed. Three major characteristics are found in the microscale shock–vortex interaction in thermal nonequilibrium: the absence of quadrupolar acoustic wave structure, which is the major feature in macroscale near-equilibrium; the increase in the dissipation rate during the strong interaction; and the decrease in enstrophy during the weak interaction. Moreover, we show that the strong shock–vortex interaction in high shock or vortex Mach numbers can cause an increase in enstrophy. We also find the viscous effect to be dominant in the net vorticity generation. Among shock and vortex parameters, the shock Mach number, vortex Mach number and vortex size turn out to play a critical role in the deformation of the vortex and the strength of interaction, which in turn govern the evolution of vorticity due to the viscous effects, the change in the dissipation rate and the increase or decrease in enstrophy during the interaction.