Floating Solids: Combining Phase Field and Fluid-Structure Interactions

Abstract

Aerodyne Research, Inc., 45 Manning Road, Billerica. MA 01821-3976 USAReceived 10 May 2004, revised 16 November 2004, accepted 20 November 2004Published online 22 April 2005Key words Phase field, fluid-structure interactions, Navier-Stokes, finite difference.AMS 04A25A mixed-stress formulation presented here combines the methodologies of phase field and fluid-structure inter-actions in order to simulate phase transformations involving moving and rotating solid bodies interacting withfluids. The Navier-Stokes equations are solved everywhere, with an additional strain tensor field overlaid on thesolid, such that elastic stress can be incorporated into the equation of motion. An additional term in the equationfor strain evolution provides rotation due to local vorticity. The results exhibit a small amount of artificial ero-sion of the solid due to nonzero normal velocity within the diffuse interface at separation points; this is discussedhere as a phenomenon common to all diffuse interface formulations incorporating convection. Two-dimensionalsimulations presented here demonstrate oscillations due to feedback between surface tension and elastic stress,and rigid body motion with particle collision and agglomeration which involves a change in the topology of thefluid-solid interface. The formulation and simulations presented here use isotropic Cahn-Hilliard free energy,and extension of the formulation to three-dimensional and anisotropic systems is straightforward. Likewise,these simulations describe linear elastic solids with Poisson ratio of 1 (equivalent to