Fluid Structure Interaction Problems:the Necessity of a Well Posed,Stable and Accurate Formulation

We investigate problems of fluid structure interaction type and aim for a formulation that leads to a well posed problem and a stable numerical procedure.Our first objective is to investigate if the generally accepted formulations of the fluid structure interaction problem are the only possible ones.Our second objective is to derive a stable numerical coupling.To accomplish that we will use a weak coupling procedure and employ summation-by-parts operators and penalty terms.We compare the weak coupling with other common procedures.We also study the effect of high order accurate schemes.In multiple dimensions this is a formidable task and we start by investigating the simplest possible model problem available.As a flow model we use the linearized Euler equations in one dimension and as the structure model we consider a spring.