Five-equation model for compressible two-fluid flow

An interface-capturing, five-equation model for compressible two-fluid flow is presented, that is based on a consistent, physical model for the flow in the numerical transition layer. The flow model is conservative and pressure-oscillation free. Due to the absence of an interface model in the capturing technique, the implementation of the model in existing flow solvers is very simple. The flow equations are the bulk-fluid equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term, to account for the energy exchange between the fluids. The physical flow model enables the derivation of an exact expression for this source term, both in continuous and in discontinuous flow. The system is solved numerically with a limited second-order accurate finite-volume technique. Linde's HLL Riemann solver is used. This solver is simplified here and its combination with the second-order scheme is studied. When the solver is adapted to two-fluid flow, the source term in the flow equations is incorporated in the Riemann solver. Further, the total source term in the cells is integrated over each cell. Numerical tests are performed on 1D shock-tube problems and on 2D shock-bubble interactions. The results confirm that the method is pressure-oscillation free and show that shocks are captured sharply. Good agreement with known solutions is obtained. Two appendices show an approximate model for shocks in physical two-phase media and a theoretical study of the interaction of shocks with plane interfaces, which is used to analyse the shock-bubble interactions