A Computational Strategy for Fluid-Structure Interaction Combining Immersed Domains and a Body-Fitted Approach

Abstract

There are many alternatives for treating the problem of a solid moving completely inside a fluid. One of them is using the fluid equations strictly in the space occupied by the fluid, and adjusting the mesh in each temporal step. If the displacements are limited a node-movement strategy without topology changes may be used to keep low the computational costs. On the other hand, for large displacements and distortion of the computational domain (as usual when modeling cardiac valves), a full remeshing may be needed. Another approach to the problem is using immersed domains: in this case the fluid mesh is fixed and the solid imposes boundary conditions on the fluid through Lagrange multipliers. In this work we present a hybrid approach: we use a single mesh for the fluid, containing the solid, without remeshing. However, we allow the movement of its nodes to adjust to the solid boundaries. In this manner, we avoid the high cost of the remeshing step, while reducing the interpolation errors produced by elements that contain partially portions of the solid. Hence, the strategy is such that the body is always fitted by the same mesh. The main difficulty of this approach is the generation of a valid mesh efficiently (without largely distorted elements), in transferring information between solid and fluid meshes, and in the interpolations needed when re-adjusting. We have obtained some preliminary results working with a parallel Navier-Stokes solver, using geometric searching techniques that allow us to keep bounded the computational costs involved.