A perspective is given on fictitious domain methods for deformable bodies that exert large motions induced by unsteady flow. In these methods an Eulerian and Lagrangian formulation are employed for the fluid and solid, respectively, and both bodies are coupled using a Lagrange multiplier. The use of a multiplier allows the solid not to be an integral part of the fluid mesh. Three variations of the fictitious domain method that have been published before, are compared to an ALE method in two numerical experiments and in conclusion the advantages, disadvantages and differences for the different approaches are discussed.

A method is presented for modelling fluid–solid interaction with large transformations of a slender solid body. The fluid flow is described by the unsteady Navier–Stokes equation, and the solid deformation is described by an incompressible hyperelastic Neo-Hookean model. Although the fluid and solid mesh are non-conformal with respect to each other, both domains can be coupled using a Lagrange multiplier. Accuracy and robustness are improved by a computationally inexpensive adaptive meshing scheme which is applied to the fluid mesh at the position of the solid interface. To illustrate the applicability of this method, 2D and 3D model problems are presented that are closely related to dynamical heart-valve computations.