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

Abstract

A mixed¯nite-element¯nite-di®erence numerical method is developed to calculate nonlinear°uid{solid interaction problems. In this study, the structure is assumed to be rigid with large motion and the°uid°ow is governed by nonlinear, viscous or non-viscous,¯eld equations with nonlinear boundary conditions applied to the free surface and°uid{solid interaction interfaces. A moving coordinate system¯xed at a point in the structure is used to describe the°uid°ow, 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 di±culties of matching°uid meshes with large solid motion. Nonlinear numerical equations describing nonlinear°uid{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.

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