A Higher-Order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid-Structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures

This manuscript presents a discontinuous Galerkin-based numerical method for solving fluid-structure interaction problems involving incompressible, viscous fluids. The fluid and structure are fully coupled via two sets of coupling conditions. The numerical approach is based on a high-order discontinuous Galerkin (with Interior Penalty) method, which is combined with the Arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain, which is not known a priori. Two strongly coupled partitioned schemes are considered to resolve the interaction between fluid and structure: the Dirichlet-Neumann and the Robin-Neumann schemes. The proposed numerical method is tested on a series of benchmark problems, and is applied to a fluid-structure interaction problem describing the flow of blood in a patient-specific aortic abdominal aneurysm before and after the insertion of a prosthesis known as stent graft. The proposed numerical approach provides sharp resolution of jump discontinuities in the pressure and normal stress across fluid-structure and structure-structure interfaces. It also provides a unified framework for solving fluid-structure interaction problems involving nonlinear structures, which may develop shock wave solutions that can be resolved using a unified discontinuous Galerkin-based approach.