Coupling of SPH-ALE method and finite element method for transient fluid–structure interaction

Abstract This article presents an interface-energy-conserving coupling strategy for transient fluid–structure interaction. The solid sub-domain is discretized by finite element method with Newmark time integrator, whereas for the fluid sub-domain we use the mesh-less method SPH-ALE with 2nd order Runge–Kutta scheme. This paper proposes a method to impose a mean interface normal velocity continuity in such a way that the algorithmic interface energy is zero during the whole period of numerical simulation. This coupling method thus ensures that the coupled problem shall be stable in time. Secondly it will converge in time with the rate of convergence of the worst time integrator chosen for each problem. The proposed method is first applied to a mono-dimensional problem by which we investigate the phenomena of propagation of shock waves across the fluid–structure interface. A good agreement is observed between the numerical result and the analytical solution in the 1D shock wave propagation test cases. Finally, a multi-dimensional example is presented and compared to another coupling approach.