# Numerical Simulation of Fluid-Structure Interaction Problems on Hybrid Meshes with Algebraic Multigrid Methods

## Dr. Huidong Yang

**March 26, 2010, 9:30 a.m. BA 9912**

Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincare operators.

This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains.

These sub-problems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time discretization implicit first order methods are used. The discretized equations are solved by algebraic multigrid methods for which a stabilized coarsening hierarchy is constructed in a proper way.

We developed a draft implementation of a grid-enabled solver for this fluid-structure interaction problem. A recently designed Client/Server model under the grid environment is used. The interface equation is solved on the server grid node, while the fluid and the structure sub-problems are solved independently on client grid nodes.