A fully coupled ALE interface tracking method for a pressure-based finite volume solver

Simulation of two-phase gas-liquid flows is a challenging problem in terms of predicting the interface position and appropriately coupling the phases. Stability restrictions induced by surface tension of the liquid phase may increase the level of difficulty of the simulation. The Arbitrary Lagrangian-Eulerian (ALE) method along with an interface tracking technique is an approach for a precise prediction of the interface position. The restrictions in the simulation due to surface tension necessitate an implicitly coupled solution algorithm. In this research, the interface kinematic condition equation is discretized in a new coupled form, including an interface displacement variable as well as the interface velocity components. Furthermore, an implicitly discretized formulation of interface curvature is implemented in the interface normal force balance to facilitate the complete coupling of the interface displacement movement to the hydrodynamic behaviour of the flow. Finally, the governing equations of both phases as well as complete set of interface equations are solved simultaneously in a system of linearized algebraic equations. A partially coupled interface tracking (PCIT) method and a fully coupled interface tracking method (FCIT) are developed and evaluated in predictions of a backward-facing step flow, of liquid falling films with and without interaction with a gas phase flow, of an oscillating drop, and of a rising bubble. The results show that in the viscocapillary regime, the FCIT method keeps its stability in a wide range of CFL numbers, whereas the PCIT method is stable only for CFL ≤1. When the surface tension is ignored in a backward-facing step flow, the PCIT method also remains stable for higher CFL number due to the coupled formulation of interface displacement and slope. The present results are in excellent agreement with previous numerical and experimental work results reported in the literature.