A pressure-based method for weakly compressible two-phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium

Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The can easily deal with different equation states and it includes relaxation terms characterized by user-defined finite parameters, which drive pressure velocity each phase toward equilibrium. There is no clear notion speed sound, thus, most classical low Mach approximation cannot be cast in this context. proposed solution strategy consists two operators: semi-implicit finite-volume solver for hyperbolic part an ODE integrator processes. Being acoustic integrated implicitly, stability condition on time step lessened. discretization non-conservative involving gradient volume fraction fulfills construction non-disturbance avoid oscillations across multimaterial interfaces. developed simulation tool validated through one-dimensional simulations shock-tube Riemann-problems, water-aluminum water-air mixtures, vapor-liquid mixture water carbon dioxide, almost pure numerical results match analytical reference ones, except some expected discrepancies shocks, however remain acceptable (errors within percentage points). All tests were performed CFL numbers greater than one, issues arose, even 10. effects values parameters amount equations state -- stiffened gas Peng-Robinson investigated.