The travelling wave scheme for the Navier-Stokes equations

A new scheme is developed for the one-dimensional, compressible Navier-Stokes equations. The method is a deviation from traditional explicit methods in that the hyperbolic and parabolic parts are treated as a single entity and travelling waves are used as approximating tools. The scheme is used mainly for computation in the regime where the mesh size is of the same order as the ratio of the viscosity epsilon to the characteristic speed. A viscous Riemann solver is designed that solves the local Riemann problems.