Development of a Coupled and Unified Solution Method for Fluid-Structure Interactions

Abstract

Traditional fluid-structure solutions usually involve the use of distinct methodologies and codes, eg., finite-volume for the fluids and finite-element for the structural dynamics [GG92]. Such a strategy consequently involves the use of sub-iterations to ensure temporal accuracy [MM98]. Alternately, a staggered solution procedure that preserves temporal accuracy without sub-iterations may be employed [FL98]. Further, coupled implicit solution schemes have also been developed [FF92]. Despite these developments, issues remain regarding the accuracy of load transfers between the fluid and structural domains as well as the robustness and efficiency of loosely-coupled solution approaches. In this article, we consider a unified formulation that employs finite-volume solutions of both the fluid and structural counterparts and a fully coupled solution of the combined system. Specific attention is paid to the formulation of the interface flux balance between the fluid and structural zones to insure appropriate flux conservation at the interface as well as full implicitness of the non-linear solution procedure. The algorithm is applied to one-dimensional fluid-structure problems to demonstrate the capabilities of the method.