A TVD WAF scheme based on an accurate Riemann solver to simulate compressible two-phase flows

Abstract

Purpose

This study aims to propose a robust total variation diminishing (TVD) weighted average flux (WAF) finite volume scheme for investigating compressible gas–liquid mixture flows.

Design/methodology/approach

This study considers a two-phase flow composed of a liquid containing dispersed gas bubbles. To model this two-phase mixture, this paper uses a homogeneous equilibrium model (HEM) defined by two mass conservation laws for the two phases and a momentum conservation equation for the mixture. It is assumed that the velocity is the same for the two phases, and the density of phases is governed by barotropic laws. By applying the theory of hyperbolic equations, this study establishes an exact solution of the Riemann problem associated with the model equations, which allows to construct an exact Riemann solver within the first-order upwind Godunov scheme as well as a robust TVD WAF scheme.

Findings

The ability and robustness of the proposed TVD WAF scheme is validated by testing several two-phase flow problems involving different wave structures of the Riemann problem. Simulation results are compared against analytical solutions and other available numerical methods as well as experimental data in the literature. The proposed approach is much superior to other strategies in terms of the accuracy and ability of reconstruction.

Originality/value

The novelty of this work lies in its methodical extension of a TVD WAF scheme implementing an exact Riemann solver developed for compressible two-phase flows. Furthermore, other novelty lies on the quantitative calculation of different Riemann problem two-phase flows. Simulation results involve the verification of the constructed methods on the exact solutions of HEM without any restriction of variables.