A physical five-equation model for compressible two-fluid flow, and its numerical treatment

A novel five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The model uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which source terms are derived from fundamental physical laws. The Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the source terms is proposed. The source terms have distinct contributions in the cell domain and at the cell faces. For the source-term evaluation at the cell faces, the Riemann solver is elegantly exploited. Numerical results are presented for shock-tube and shock-bubble-interaction problems. The resemblance with experimental results is very good. Free-surface pressure oscillations do not occur, without any precaution. The paper contributes to state of the art in computing two-fluid flows.