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. AMS subject classifications: 65M12, 65M06,65M30,65M20,74F10,35Q35