A mixed finite-element finite-difference method for nonlinear fluid-structure interaction dynamics. I. Fluid-rigid structure interaction

A mixed finite-element finite-difference numerical method is developed to calculate nonlinear fluid-solid interaction problems. In this study, the structure is assumed to be rigid with large motion and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. A moving coordinate system fixed at a point in the structure is used to describe the fluid flow, and for numerical analysis purposes, an arbitrary Lagrangian-Eulerian mesh system is constructed relative to this moving system. This provides a convenient method of overcoming the difficulties of matching fluid meshes with large solid motion. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. A selection of numerical examples illustrates the developed mathematical model and through numerical simulations it is shown that the proposed approach is practical and useful