Interface tracking finite volume method for complex solid–fluid interactions on fixed meshes

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Abstract
We present a numerical technique for computing flowfields around moving solid boundaries immersed in fixed meshes. The mixed Eulerian–Lagrangian framework treats the immersed boundaries as sharp solid–fluid interfaces and a conservative finite volume formulation allows boundary conditions at the moving surfaces to be exactly applied. A semi‐implicit second‐order accurate spatial and temporal discretization is employed with a fractional‐step scheme for solving the flow equations. A multigrid accelerator for the pressure Poisson equations has been developed to apply in the presence of multiple embedded solid regions on the mesh. We present applications of the method to two types of problems: (a) solidification in the presence of flows and particles, (b) fluid–structure interactions in flow control. In both these problems, the sharp interface method presents advantages by being able to track arbitrary interface motions, while capturing the full viscous, unsteady dynamics. Copyright © 2001 John Wiley & Sons, Ltd.