Simulation of gas-liquid two-phase flow based on the Riemann problem

Abstract

This contribution report on recent scientific methodologies concerning compressible gas-liquid two-phase mixture. Within this context, a one-dimensional set of three partial differential equations that takes account of the velocity nonequilibrium between the two phases is used. Motivated by the hyperbolicity and conservativity features of these equations, a closed-form theoretical solution has provided key insights into the Riemann problem for the gas-liquid two-phase mixture. In addition to that, the proposed theoretical solution, that is an exact Riemann solver, calculates the entire wave structure including the middle states of the mixture and phases of the flow. To this end, the exact Riemann solver guarantees that the system of partial differential equations is independent of the type of the numerical technique used to validate it. Consequently, the model equations are solved numerically using Godunov methods of the upwind-type based upon the proposed exact Riemann solver. Sample academic simulations are performed and validated against analytical observations for the gas-liquid two-phase mixture. Through these simulations, we compare the predicted results with other numerical methods such as the Riemann-free solvers. Excellent agreement is observed between the analytical and numerical simulations.