Fluid Structure Interaction Problems: The Necessity of a Well Posed, Stable and Accurate Formulation (Communications in Computational Physics, 2010)
We investigate problems of fluid structure interaction type and aim for aformulation that leads to a well posed problem and a stable numerical procedure. Ourfirst objective is to investigate if the generally accepted formulations of the fluid structureinteraction problem are the only possible ones. Our second objective is to derivea stable numerical coupling. To accomplish that we will use a weak coupling procedureand employ summation-by-parts operators and penalty terms. We compare theweak coupling with other common procedures. We also study the effect of high orderaccurate schemes. In multiple dimensions this is a formidable task and we start by investigatingthe simplest possible model problem available. As a flow model we use thelinearized Euler equations in one dimension and as the structure model we consider aspring.