Linearized Navier-Stokes Solution of the Richtmyer-Meshkov Instability

Results are presented from a numerical investigation of the two-dimensional Richtmyer-Meshkov instability, using a linearization about a fully-resolved, 1-D numerical solution of the Navier-Stokes equations. An asymptotically-stable, non-dissipative, fourth-order finite-difference scheme is used with local grid refinement to properly resolve the internal structure of all shocks and the contact zone. Detailed results are shown for the case of a single fluid with constant viscosity and heat conductivity, $\rm{Pr} = 3/4$, and incident shock Mach number 1.2, across a range of contact-zone perturbation wavenumbers.