Volume-of-solid immersed boundary method for free surface flows with arbitrary moving rigid bodies

Abstract

The focus of the present work is to develop a robust algorithm for simulation of stationary/moving rigid solid object(s) in free surface flows. The algorithm is based on incompressible finite volume hybrid staggered/non-staggered framework and captures the fluid–fluid interface using the Volume-of-Fluid (VOF) method by solving advection equation for volume fraction with velocity obtained from the Navier–Stokes equations. A novel interface capturing scheme CUIBS (Cubic upwind interpolation blended scheme) is employed to preserve the sharpness of the interface. Presence of the object(s) are accounted through solid fraction, which is advected with the object velocity, either prescribed or calculated from the equations of solid dynamics. A diffuse interface immersed boundary method is employed to solve the normal momentum equation. The present formulation gives liberty to execute normal momentum and pressure correction equation every where in the domain, considering imaginary fluid inside the solid object with dynamic viscosity of heaviest fluid and density of lightest fluid. The algorithm is applied to the benchmark problems involving the flow past a stationary cylinder and water entry of a cylinder. The numerical experiment on the sedimentation of two particles is investigated to analyse the efficacy of present algorithm.