Fluid-Structure Interaction
In this text, 9 case studies examine mathematical and numerical models for studying the interaction of a fluid and a structure in a mechanical system.
TABLE OF CONTENTS Fluid-Structure Interaction
Chapter 3: Deriving Adequate Formulations for Fluid-Structure Interaction Problems: From ALE to Transpiration
Overview
Thierry Fanion
Dassault Aviation and INRIA, Saint-Cloud, France
Miguel Fern ndez
INRIA Rocquencourt, Le Chesnay, France
Patrick le Tallec
Ecole Polytechnique, Palaiseau, France
1. Introduction
Low speed large displacement problems when a flexible elastic structure interacts with the flow of an external or internal fluid occur frequently in practice, for example when studying hydraulic shock absorbers, biomedical flows in flexible pipes, aero-elastic instabilities of flexible aircraft or tall bridges, or ocean flows around very long risers. The numerical challenge is to predict the longterm time evolution and stability of these coupled systems. It turns out that enforcing the kinematic compatibility at the fluid-structure interface and updating the geometry of the fluid domain requires particular care, especially when this must be carried out within a numerical model which has been discretised in time and space.
The key is to properly respect mass and momentum conservation laws for the coupled fluid-structure system considered as a unique continuous medium sticking together because of a kinematic constraint mechanically imposed at the fluid-structure interface ? s ( t). These conservation laws when transported on a global fixed reference configuration define the mechanical problem to be solved (section 2). Consistent time discretisations can then be introduced (section 3). The problem is that, as observed in section 4, classical time integration schemes may lose their long term stability properties when used for moving domains, depending on the grid deformation smoothness and on the discretisation error in the mass equation.
To overcome all technical difficulties arising...
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