Traveling wave solutions for finite scale equations

Finite scale equations are coarse-grained PDEs that describe the evolution of density, momentum and energy fields averaged over finite intervals of space and time. These analytic equations have been found to be a useful model for analyzing and verifying discrete algorithms employed in numerical simulation. In this paper, we derive traveling wave solutions for finite scale shocks and compare the results with averaged solutions of Navier–Stokes. We find that the finite scale equations accurately predict the shock speed and width and the jump conditions relating the pre and post shock states.