### Monday, 11 October 2004 - 5:10 PM

### This presentation is part of : Rajagopal Symposium

### Numerical solution of fluid-structure interaction with applications in biomechanics

**Jaroslav Hron**, Institute of Applied Mathematics, LS III, University of Dortmund, Institute of Applied Mathematics, LS III, University of Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany
In bioengineering applications problems of flow interacting with elastic solid are very common. We formulate the problem of interaction between an incompressible fluid and an incompressible elastic material in the arbitrary Lagrangian-Eulerian formulation, including the possibility that the constitutive relations for both materials can be more general, e.g. shear-dependent viscosity in the fluid or visco-elastic behavior of the solid part. The most common approach to solve such problems of fluid structure interaction is to decouple the problem on the continuous level and perform the discretization and solution steps separately for the fluid and solid parts with weak coupling. While this approach is appropriate in some cases where the characteristic behavior of one of the components is significantly different from the other component. (i.e. the characteristic response time) There are many applications, for example in biomechanics of soft tissues, where this is not the case and the coupling needs to be incorporated in the solution process more strongly. We present a monolithic algorithm to solve the problem of time dependent interaction between an incompressible viscous fluid and an incompressible elastic solid. The continuous formulation of the problem and its discretization is done in a monolithic way, treating the problem as one continuum. We discuss some possible efficient strategies of setting up and solving the resulting systems.

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