A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows

Discretizations of two-fluid flow problems in conservative formulation generally exhibit pressure oscillations. In this work we show that these pressure oscillations are induced by the loss of a pressure-invariance property under discretization, and we introduce a non-oscillatory conservative method for barotropic two-fluid flows. The conservative formulation renders the two-fluid flow problem suitable to treatment by a Godunov-type method. We present a modified Osher scheme for the two-fluid flow problem. Numerical results are presented for a translating-interface test case and a shock/interface–collision test case.