TREATMENT OF INTERFACE PROBLEMS WITH GODUNOV-TYPE SCHEMES

A correction is proposed of Godunov-type schemes, yielding a perfect c apture of contact discontinuities in hydrodynamic flows. The correctio n method is based upon the following simple idea: If an Euler scheme i s employed starting from a non-degraded solution at a certain instant of time, the presence of a discontinuity will entail, at the next inst ant, the degradation of the solution at the two points adjacent to the discontinuity only. On the other hand, an exact solution of the Riema nn problem yields the state variables on both sides of the discontinui ty; then, the altered values at the nodes affected by numerical diffus ion can be corrected. The method is applied to problems involving a ga s-liquid interface. The liquid is supposed to be compressible, obeying an equation of state of the ''Stiffened Gas'' type, for which a solut ion to Riemann's problem is readily obtained.