Monolithic Approach for Fluid-Structure Interaction Based on Consistent Pressure Poisson Equation

Abstract

This paper describes a new monolithic approach based on the Pressure Poisson Equation (PPE) to solve interaction problems of incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equation system for the fluid-structure interaction (FSI). Based on this approach, we develop two efficient monolithic methods. In both methods, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all the other unknown variables are derived fully explicitly or partially explicitly. The coefficient matrix of the PPE for the FSI has characteristics of (a) symmetric and positive definite feature, (b) reduction of degrees of freedoms to be solved, and (c) less dependence of the condition on material properties. The arbitrary Lagrangian Eulerian method is employed for the fluid to take into account the deformable fluid structure interface. To demonstrate fundamental performances of the proposed approach, the developed two monolithic methods are applied to simulate the vibration of a rectangular cylinder induced by vortex shedding.