Aim

Fluid structure interaction problems occur in many applications of daily life: in the aerodynamics of cars and planes, in biomedical sciences or in filter techniques. For the solution of the fluid and solid equations there already exist efficient numerical methods, like the Finite Element Method and the Lattice-Boltzmann Method. But for the solution of interaction problems these methods have to be combined.

Undeformierte Membran

The diverse domains of interaction problems are ruled by different properties. Therefore, it is often computationally more efficient or sometimes even unavoidable to apply various meshes, according to the numerical method and the features of the differential operator describing the different equations governing the subdomains. Our goal is to couple the different meshes along the interfaces.

Solution

Deformierte Membran

For this coupling we use the mortar element method, a domain decomposition method that can be coupled with standard approximation techniques such as the spectral or the finite element method (more details can be found e.g. in C. Bernadi, Y. Maday, A. T. Patera: "A new nonconforming approach to domain decomposition: the mortar element method", Paris, Cambridge).
Starting from the boundary value problems on the various subdomains, we have to find transmission conditions, which relate the problems to each other along the interfaces. With these interface conditions, the whole problem (governing equations as well as boundary and transmission conditions) can be formulated in the weak sense (an introduction into the formulation of fluid structure interactions problems is given in C. Grandmont, Y. Maday: "Nonconforming Grids for the Simulation of Fluid-Structure Interaction", 1991).

Benefit

Nichtkonforme Netze

The mortar element method makes it possible to couple DDFEM and ParPac, two efficient solid and fluid solver, respectively. By coupling these two solvers, we can benefit from the advantages of both and get an efficient solution for fluid structure interaction problems.