A THINC-based numerical model for incompressible flows with free surfaces on the overset grids: On preserving accuracy and conservation of volume fraction

Abstract

In this paper, we develop an accurate and robust numerical model for incompressible multiphase flows with free surface on the unstructured overset grids within the framework of OpenFOAM. To capture the moving interface between two immiscible fluids, THINC/QQ (THINC method with quadratic surface representation and Gauss quadrature) scheme is presented on the static and dynamic overset grids using the volume of fluid (VOF) method. A novel interpolation algorithm is proposed to transfer the volume fraction across the overset grids, which significantly improves the geometric faithfulness and numerical conservation of free surfaces since the interface is reconstructed and represented as quadratic surface in the fringe cells of the overset grids using the THINC formulation. A pseudo-Laplacian approach is utilized to interpolate both the velocity and pressure fields across overset grids achieving a second-order accuracy. The incompressible Navier–Stokes equations are solved together with a transport equation of volume fraction using second-order finite volume schemes, which then is coupled with the motion solver during each time step to obtain converged solution between the hydrodynamic flow and kinematic motion of the rigid body. The so-called thincFoam/overset, when used in the transient simulation of interfacial multiphase flows, provides high-fidelity solutions with an order of magnitude reduction in the conservation error of volume fraction field. Numerical verifications have been carried out through various 2D and 3D benchmark tests, such as the water entry of a wedge, floating structure in regular waves, and water entry of a horizontal cylinder. The numerical results demonstrate that the present model shows great potential in capturing complex moving interfaces undergoing large deformations and topological changes with excellent conservation for simulating the nonlinear interaction between multiphase flows and solid structures.