Three-dimensional fluid structure interaction between a compressible fluid and a fragmenting structure with a conservative immersed boundary method

In this work, we present a conservative method for three-dimensional inviscid fluid-structure interaction problems. On the fluid side, we consider an inviscid Euler fluid in conservative form. The Finite Volume method uses the OSMP high-order flux with a Strang operator directional splitting [1]. On the solid side, we consider an elastic deformable solid with possible fragmentation. We use a Discrete Element method (particles connected with springs) for the discretization of the solid [2]. Body-fitted methods are not wellsuited for large displacements or fragmentation of the structure, since they involve possibly costly remeshing of the fluid domain. We use instead an immersed boundary technique through the modification of the finite volume fluxes in the vicinity of the solid. The method is tailored to yield the exact conservation of mass, momentum and energy of the system and exhibits consistency properties [3, 4]. In the event of fragmentation, void can appear due to the velocity of crack opening. Since the high-order OSMP numerical flux is not stable in the presence of void, we resort locally to the Lax-Friedrichs flux near cracks [5]. Since both fluid and solid methods are explicit, the coupling scheme is designed to be explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. It should be noted that the coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. We also address boundary conditions and their influence on stability and accuracy. We will present numerical results showing the robustness of the method in the case of a fragmenting solid coupled with a compressible fluid flow.