Simulations of free-surface flows with an embedded object by a coupling partitioned approach

Abstract

This article describes numerical investigations of the flow and wave patterns under stationary or moving submerged objects in a viscous fluid. To incorporate the effects of the free motion objects as well as the free surface, the modified height function scheme is implemented to accurately capture the configurations of free surfaces. For dealing with complex submerged objects in the fluid, a hybrid Cartesian/immersed boundary method is adopted to allow imposition of the solid boundary conditions with a linear interpolation approach. The considered physical model is developed for incompressible, unsteady free-surface flows to satisfy the condition of volume conservation based on the staggered finite-difference spatial discretization. Possible free-surface configurations are described by a high-order flux corrected transport model to maintain the sharp interface and in the mean time to eliminate the surface numerical oscillations. Finally several examples are provided to assess the performance of the developed numerical model. Four numerical validated examples are used to respectively demonstrate the proposed schemes. They are (1) the flow past a circular cylinder, (2) in-line oscillating circular cylinder in a fluid, (3) liquid sloshing in a partially filled rectangular tank and (4) the oscillatory sloshing tank over a shaking table to test the total volume preservation. In addition, two more numerical experiments are carried out to simulate (5) the free-surface flows with the embedded solid body subject to stationary horizontal cylinder and (6) free-surface simulations induced by an oscillating moving object. Both tested cases show encouraging results as well by the present algorithm.