Fluid-solid interaction by non-conforming mesh methods

This thesis aims to better understand the numerical approximation of the uid-solid interaction that involves large deformations and displacements of an immersed solid within the ow eld. It can be applied as an engineering tool for improving mechanical component design that typically leads to various numerical and algorithmic challenges. The numerical strategy in this thesis uses xed and non-conforming mesh methods due to their ability to solve the uid ow in a static mesh even with considerable displacements of internal boundaries. But several other numerical ingredients are developed in this work to overcome instability issues that may appear in the numerical solution and to make a nordable such computation. One is the application of the Variational Multi-Scale (VMS) framework to construct a stable discrete formulation of the incompressible ow equations. Others have to do with non-conforming mesh methods.