Commun. Comput. Phys., 8 (2010), pp. 1111-1138.


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

Jan Nordstrom 1*, Sofia Eriksson 2

1 School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, WITS 2050, South Africa; Department of Aeronautics and Systems Integration, FOI, The Swedish Defense Research Agency, SE-164 90 Stockholm, Sweden; and Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
2 Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.

Received 26 April 2009; Accepted (in revised version) 12 February 2010
Available online 23 June 2010
doi:10.4208/cicp.260409.120210a

Abstract

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

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Key words: Fluid structure interaction, well posed, finite difference, high accuracy, stability.

*Corresponding author.
Email: Jan.Nordstrom@it.uu.se (J. Nordstrom), sofia.eriksson@it.uu.se (S. Eriksson)
 

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