A 3D collision scheme for compressible media in a general connectivity Lagrangian formulation

摘要

In multi-material hydrodynamic problems described using the Lagrangian formulation, the interaction between different material meshes is carried out using collision schemes. The basic schemes simulate interactions using momentum transfer equations, which are solved for every pair of colliding meshes. In this paper we present a novel collision scheme, which extends the basic ones. After completing the momentum transfer stage, our scheme prevents penetration between meshes gradually, while detecting future collisions, ensuring that the penetration depth is kept under a specified limit. Collisions of more than two meshes at the same point are treated specifically, by solving vectorized momentum transfer equations. This approach, which suppresses sliding for these points, prevents numerical penetrations of mesh vertices into the interface between two other meshes. Since this special treatment is invoked only when it is necessary, it does not significantly affect the efficiency of the scheme. We demonstrate the generality of our scheme in a problem in which one mesh is calculated using a Lagrangian code, while the other mesh is calculated concurrently using an ALE code. The two meshes are coupled using our collision scheme, by passing information between them (and the codes), and by updating their boundaries' position and velocity.