SPH and ALE Formulations for Fluid Structure Coupling

Abstract

Simulation of Fluid Structure Interaction FSI, problems becomes more and more the focus of computational engineering, where FEM (Finite element Methods) for structural mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic). Up to these days very little has been done to compare different methods and assess which one would be more suitable. For small deformation, FEM Lagrangian formulation can solve structure interface and material boundary accurately; the main limitation of the formulation is high mesh distortion for large deformation and moving structure. One of the commonly used approach to solve these problems is the ALE formulation which has been used with success in the simulation of fluid structure interaction with large structure motion such as sloshing fuel tank in automotive industry and bird impact in aeronautic industry. For some applications, including bird impact and high velocity impact problems, engineers have switched from ALE to SPH method to reduce CPU time and save memory allocation. In this paper the mathematical and numerical implementation of the ALE and SPH formulations are described. From different simulation, it has been observed that for the SPH method to provide similar results as ALE or Lagrangian formulations, the SPH meshing, or SPH spacing particles needs to be finer than the ALE mesh. To validate the statement, we perform a simulation of a shock wave propagation generated by explosive detonation. For this simple problem, the particle spacing of SPH method needs to be at least two times finer than ALE mesh. A contact algorithm is performed at the fluid structure interface for both SPH and ALE formulations.