Treatment of interface problems with Godunov-type schemes
A correction is proposed of Godunov-type schemes, yielding a perfect capture of contact discontinuities in hydrodynamic flows. The correction method is based upon the following simple idea: if an Euler scheme is employed starting from a non-degraded solution at a certain instant of time, the presence of a discontinuity will entail, at the next instant, the degradation of the solution at the two points adjacent to the discontinuity only. On the other hand, an exact solution of the Riemann problem yields the state variables on both sides of the discontinuity; then, the altered values at the nodes affected by numerical diffusion can be corrected. The method is applied to problems involving a gas-liquid interface.
scientific article; zbMATH DE number 947022