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.