Lid driven cavity with a flexible bottom surface Michael Alletto

• contributor: Michael Alletto
• affiliation: WRD MS
• contact: click here for email address
• OpenFOAM versions: v2112
• Published under: CC BY-NC-ND license (creative commons licenses)

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You can download the case https://gitlab.com/mAlletto/openfoamtutorials/-/tree/master/membranBCSend/testCases/nonLinMembraneStaightDisplacement/lidDrivenCavity] here.

Introduction

In this small tutorial we will see how to simulate a fluid structure interaction problem with the membrane boundary conditon shown in the tutorial https://wiki.openfoam.com/Coupling_a_simple_nonlinear_membrane_to_point_displacement_Michael_Alletto. The test case consists in the well kown lid driven flow. In order to allow for fluid structure interaction (FSI) the bottom wall is flexible. The same test case was already used in order to validate a number of FSI codes (see e.g. [1]-[3]).

Setup

The setup of the simulation is shown in the following figure. It consists in a lid driven cavity case with some modifications. The difference to the classical case are the following: The bottom wall is flexible and is allowed to deform. The top wall is moving with a time varying velocity:

U = 1 - cos (2 pi t / 5).

The above boundary condition was implemented by using an expFixedValue boundary condition:

References

[1] Jean-Frédéric Gerbeau and Marina Vidrascu. A quasi-newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows. ESAIM: Mathematical Modelling and Numerical Analysis, 37(4):631–647, 2003.

[2] Christophe Kassiotis, Adnan Ibrahimbegovic, Rainer Niekamp, and Her- mann G Matthies. Nonlinear fluid–structure interaction problem. part i: implicit partitioned algorithm, nonlinear stability proof and validation examples. Computational Mechanics, 47:305–323, 2011.

[3] Jesús Gerardo Valdés Vázquez. Nonlinear analysis of orthotropic mem- brane and shell structures including fluid-structure interaction. 2007.