Coupling of stabilized total Lagrangian and weakly compressible SPH models for challenging fluid–elastic structure interaction problems

Abstract

A numerical model based on the total Lagrangian (TL) and weakly compressible (WC) smoothed particle hydrodynamics (SPH) coupling is developed for complex hydroelastic FSI problems. In this coupling scheme, the fluid phase is based on the WCSPH formulation improved by a numerical diffusion term. A TLSPH framework, stabilized by the hourglass control scheme and artificial viscous force, is employed for the solid phase, based on a linear-elastic constitutive model. The proposed model is verified using a variety of benchmark tests involving the free oscillation of a cantilever plate, the hydrostatic water column on an elastic plate, and dam-break flows interacting with deformable solid domains. In addition, the effect of time integration on the solution accuracy of the proposed model is investigated using two different time-integration schemes in the literature with/without a predictor-corrector stage required for multiple calculations in each time step. Comparisons indicate that the proposed model computations obtained with both time-integration schemes have a reasonable agreement with experimental and other numerical model results and provide smooth pressure/stress fields without numerical instability thanks to special treatments. Although numerical computations obtained with both of the time-integration schemes are generally quite similar, it is observed that the time-integration scheme with a predictor-corrector stage provides higher stability in specific cases.