Based on operator splitting technique, Euler equations is splitted into convection part and non-convection part. A predicted solution is obtained by solving the convection part with explicit GFM method. It is corrected by an implicit pressure correction algorithm derived from the non-convection part. A second order primitive explicit-implicit algorithm is built. It shows that CFL condition can be relaxed and efficiency is improved.

In conventional ghost fluid method,Riemann problems are defined by taking direatly states at grid points as initial conditions.In this article,we improve this approach by taking states at interpolated points as initial conditions.States at interpolated points are obtained by area average of states at four surrounding grid points.Since initial conditions are smooth,our method gives results with less numerical oscillations.Numerical experiments illustrate that the method is effective.