Restoring monotonicity of slowly-moving shocks computed with Godunov-type schemes

We tackle, using the Isothermal Gas Equations, the problem of loss of monotonicity behind slowly moving shock waves as computed by Godunov-type schemes. A parameter by which slow-shocks can be detected within a flow-field is presented, along with a modification of Godunov’s scheme that introduces numerical dissipation into the flow to damp the oscillations. We also extend the scheme to second order in smooth flow.