Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids

We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes. In particular, we consider a method where the fluid mesh (on the background) is fixed, apart from the interface with the moving immersed structure, where general polygonal elements of arbitrary shape and changing in time are generated. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to a heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement. We finally present some numerical results with the aim of showing the effectiveness of the proposed method.