Numerical Modeling of Liquid-Vapor-Gas Flows with Arbitrary-Rate Mass Transfer

We are interested in the modeling of liquid-vapor-gas flows with phase transition. We describe these flows by a hyperbolic single-velocity three-component compressible flow model with instantaneous pressure relaxation that we studied in previous work. The model includes thermal relaxation terms to account for heat transfer, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases. To numerically solve the model system we use a fractional step method where we alternate between the solution of the homogeneous system via finite volume HLLC-type schemes and the solution of systems of ordinary differential equations that take into account the relaxation source terms. In this work we propose a novel numerical procedure for chemical relaxation that can efficiently describe arbitrary-rate mass transfer, both slow finite-rate processes and stiff instantaneous ones. The method is applicable to an arbitrary equation of state. The idea consists in describing the relaxation process by a system of ordinary differential equations that admits an analytical semi-exact exponential solution. Some numerical experiments are presented to show the effectiveness of the proposed method.