A multi-moment finite volume formulation for the interaction between free surface flow and moving bodies with THINC method

Abstract

A numerical model is developed for fluid-rigid body interaction involving free surfaces on moving unstructured grids using the Arbitrary-Lagrangian–Eulerian (ALE) formulation. The multi-moment finite volume method is used for the spatial discretization of Navier–Stokes equations in which volume integrated average (VIA) and point values (PVs) are defined as prognostic variables and updated by integral and differential form respectively. Given VIA and PV in each cell, a higher-order reconstruction function can be built in a compact stencil which improves the numerical accuracy and robustness on the unstructured grids. More importantly, it facilitates imposing a more accurate Dirichlet–Neumann condition for the partitioned interface between the fluid and solid region. The geometrical conservation law (GCL) is also formulated to govern the spatial volume element under an arbitrary mapping. In order to capture the free surfaces of multiphase flows, the volume-of-fluid (VOF) equation is solved by THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) scheme in varying mesh, which achieves geometrical faithful interface representation, particularly for curved surfaces in a complex and moving domain. The present model is validated by some benchmark tests in two dimensions for fluid–structure interaction problems with free surfaces. The numerical results show closer agreement with the experimental data than the reference solution of other numerical models. It convinces that the present model provides accurate and robust solutions for the simulation of the complex interaction between the free surface flows and moving bodies.