An Eulerian-Lagrangian approach for large deformation fluid structure interaction problems, Part 1: algorithm development

A numerical algorithm for tightly coupled, high-deformation fluid-structure interaction problems is presented. The foundation of the method is the integration of a Lagrangian particle technique (the Material Point Method, or MPM) with a multimaterial 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 computed 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.