Efficient solution strategies for fluid-structure-interactions have to take into account the couplings within the multi-field problem. If fluid and structure are solved successively, the surface tension is to be evaluated within the solution strategy for strong coupled interactions, as displayed below. This may lead to divergence of the solution vectors in the fluid and the solid domain, if the interaction in-between becomes relevant.
For a scaled up radius of convergence, space-time finite element formulations are used, which describe the kinematics of fluids and solids by the velocities as primary variables. The consistent formulation allows for a simultaneous solution of the whole problem, avoiding additional transition conditions between the two domains.
For a quadratic convergence within the Newton-Raphson scheme, the linearization of the discretized model equations of fluid-structure interactions has to consider the changing fluid mesh. The displayed system of equations shows the dependencies in the multi-field problem and the strong coupling between fluid and solid. Furthermore the kinematic coupling of a pseudo-structure adapting the deformable structure and the moving fluid mesh can be regarded.
Example: Fluid-induced deformations of an elastic plate
The moving finite element mesh is plotted nearby the elastic plate for a selected deformation state
The displayed velocity-field indicates the interaction between the flexible plate and the passing fluid.