An Eulerian-Lagrangian approach for large deformation fluid structure interaction problems, part 2: Multi-physics simulations

A numerical algorithm for tightly coupled, high-deformation fluid-structure inter-action problems is presented. The foundation of the method is the integration of a Lagrangian particle technique (the Material Point Method, or MPM) with a multi-material Eulerian code. In this approach, each material is described and evolves in its preferred reference frame (e.g., Lagrangian for solids, Eulerian for fluids). The MPM uses a background mesh to update particle states. By using the Eulerian multi-material mesh as the background mesh to update particle states, the solid materials have a dual representation in the Lagrangian and Eulerian frame. It is in this common reference frame that coupling interactions among materials are com-puted through momentum and energy exchange terms in the multi-field equations. The approach is outlined and results from a numerical order-of-accuracy study are presented. Simulation results are compared with known solutions for the stress distribution in a pressurized cylinder. It is shown that the combined approach has the same order-of accuracy as the stand-alone material point method and gives excellent agreement with exact solutions for this geometry.