Numerical solution for hyperbolic conservative two-phase flow equations

We outline an approximate solution for the numerical simulation of two-phase fluid flows with a relative velocity between the two phases. A unified two-phase flow model is proposed for the description of the gas–liquid processes which leads to a system of hyperbolic differential equations in a conservative form. A numerical algorithm based on a splitting approach for the numerical solution of the model is proposed. The associated Riemann problem is solved numerically using Godunov methods of centered-type. Results show the importance of the Riemann problem and of centered schemes in the solution of the two-phase flow problems. In particular, it is demonstrated that the Slope Limiter Centered (SLIC) scheme gives a low numerical dissipation at the contact discontinuities, which makes it suitable for simulations of practical two-phase flow processes