Resolving the Shock Wave Profile in Viscous Fluids

Capturing and modeling shock wave profiles has a long history in computational analysis. Often artificial irreversibilities and/or smearing schemes are implemented in order to stabilize and resolve the shock. This work presents a direct numeric simulation of the full Navier-Stokes equations where the shock profile is completely resolved without the use of artificial viscosity or shock smearing techniques. Several viscosity models are employed to study the role of viscosity on this second order accurate finite difference scheme. The results are compared to an analytic solutions and experimental results. The results indicated that the shock front thickness and entropy production are in good agreement with simple analytic solutions and experimental results. The extension of this technique to solid and granular materials will be discussed.