Well Posed, Stable and Weakly Coupled Fluid Structure Interaction Problems

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 FSI problems are the only possible ones. Our second objective is to derive a numerical coupling which is truly stable. To accomplish that we will use a weak coupling procedure and employ summationby-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 for that reason 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.