Efficient three-equation two-phase model for free surface and water impact flows on a general curvilinear body-fitted grid

Abstract

In this work, a simple and efficient three-equation two-phase model is transformed to a multi-dimensional general curvilinear coordinate system for simulation of free surface and water impact flows on curvilinear body-fitted grids. The two-phase model is a reduced version of the Baer–Nunziato model for compressible multiphase flows, in which the governing equations for only the liquid phase are active, whereas those for the air phase are neglected. The CPU cost is significantly reduced by solving the equation system only in the liquid regions, instead of solving the entire computational domain as in classical Euler approaches. The physical system is formulated in a hyperbolic vector form in a curvilinear coordinate system and solved using a monotonic upstream-centered scheme for conservation laws (MUSCL)/Godunov-type finite volume scheme. Compressive MUSCL limiters combined with the high-order finite volume approach result in a sharp interface solution. Validations with numerical grid refinement and convergence studies on dam-break and water impact problems are addressed, and the capability and robustness of the present model for accurate simulation of free surface and water impact flows are demonstrated. The implementation of the present system on a curvilinear body-fitted grid and the use of the Tait equation of state for water for the closure of the compressible system allow the method to solve water impact flow problems with both low-speed and high-speed complex geometries in industry and engineering.