A Phasic WAF-HLLC Scheme for the Compressible Two-Fluid Model on a Quadrilateral Unstructured Grid

Abstract

In this article, we develope a second-order-accurate phasic WAF-HLLC scheme for the compressible two-fluid model in two dimensions. First, we derive a new phasic HLLC scheme for the two-fluid model by assuming the phasic velocities are close to each other, Second, the WAF (weighted-average flux) procedure is applied separately to the numerical flux of the gas phase, to the numerical flux of the liquid phase, and to the numerical void fraction at the cell interface. To treat the complex geometries of the two-phase problem, the scheme deploys a quadrilateral unstructured grid. The total variation diminishing (TVD) constraint is implemented in order to remove the spurious oscillation near a large gradient of the solution that is observed using the original WAF scheme. We solve several test two-phase flow problems by the present phasic WAF-HLLC scheme, including the 2-D shock–bubble interaction and the supercavitating high-speed underwater projectile. The present scheme demonstrate robustness and accuracy.