Commun. Comput. Phys., 15 (2014), pp. 1266-1290.


An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

M. Bergmann 1*, J. Hovnanian 1, A. Iollo 1

1 Inria, F-33400 Talence, France, Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France, CNRS, IMB, UMR 5251, F-33400 Talence, France.

Received 22 March 2013; Accepted (in revised version) 11 October 2013
Available online 14 February 2014
doi:10.4208/cicp.220313.111013a

Abstract

An accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

AMS subject classifications: 68Uxx, 76

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Key words: Viscous incompressible flow, immersed boundary method, penalty method, cartesian grid, self-propelled jellyfish.

*Corresponding author.
Email: michel.bergmann@inria.fr (M. Bergmann), jesshovna@msn.com (J. Hovnanian), angelo.iollo@math.u-bordeaux1.fr (A. Iollo)
 

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