A partitioned approach for the coupling of SPH and FE methods for transient nonlinear FSI problems with incompatible time-steps

We propose a method to couple smoothed particle hydrodynamics and finite elements methods for nonlinear transient fluid-structure interaction simulations by adopting different time-steps depending on the fluid or solid sub-domains. These developments were motivated by the need to simulate highly non-linear and sudden phenomena requiring the use of explicit time integrators on both sub-domains ( explicit Newmark for the solid and Runge-Kutta 2 for the fluid). However, due to critical time-step required for the stability of the explicit time integrators in, it becomes important to be able to integrate each sub-domain with a different time-step while respecting the features that a previously developed mono time-step coupling algorithm offered. For this matter, a dual-Schur decomposition method originally proposed for structural dynamics was considered, allowing to couple time integrators of the Newmark family with different time-steps with the use of Lagrange multipliers. Copyright (C) 2016 John Wiley & Sons, Ltd.