An immersed boundary method for geometrical shock dynamics

Abstract

A new algorithm is presented for the resolution of the Geometrical Shock Dynamics model in presence of obstacles in an Eulerian framework. The numerical method relies on a Fast-Marching like algorithm on a Cartesian grid, which allows dealing with complex geometrical configurations and shock waves interactions at a reduced computational cost. The application of an homogeneous Neumann condition at the border of rigid obstacles, not aligned with the mesh, is based on the Immersed Boundary Method. For a given obstacle, a set of ghost points is defined in the solid area and the corresponding unknown flow parameters are updated using a compatibility condition. A good agreement is observed between numerical results, experimental data and CFD simulations, both in 2D and 3D, which demonstrates the validity and the capabilities of this method.