A new method for simulating rigid body motion in incompressible two-phase flow

Computational treatment of immersed rigid bodies, especially in the presence of free surfaces and/or breaking waves, poses several modeling challenges. A motivating example where these systems are of interest is found in offshore wave energy harvesting systems, where a floating structure converts mechanical oscillations to electrical energy. In this study, we take the first step in developing a robust computational strategy for treating rigid bodies with possible internal dynamics, such that they may be fully coupled to a fluid environment with free surfaces and arbitrarily large fluid motion. Many schemes for fluid-solid interaction involve formulating and solving all of the equations of motion on a structured cartesian finite difference grid, but with overlaying Lagrangian representation of the solid that is used to track its position. Ultimately, most of these techniques, which include methods for deformable solids as well, solve the equations of motion completely on the Eulerian grid (see, for example, (J. Comput. Phys. 2005; 205:439-457) and (J. Comput. Phys. 2008; 227:3114-3140)). By contrast, we solve Lagrangian-type rigid body equations coupled with the Eulerian formulation of the Navier Stokes equations for an immersed solid. This departure from the standard method facilitates the addition of the internal dynamics characteristic of power conversion systems. The study is based on a finite difference and level set description of a free surface between two immiscible fluids (for example water and air) for incompressible flow by Summan (J. Comput. Phys. 1994; 114:146-159). © 2010 John Wiley & Sons, Ltd.