An Initial and Boundary Value Problem Modeling Fish-like Swimming
Résumé
In this paper we consider an initial and boundary value problem modeling the self-propelled motion of solids in a bi-dimensional viscous incompressible fluid. The self-propelling mechanism, consisting in appropriate deformations of the solids, is a simplified model for the propulsion mechanism of fish-like swimmers. The governing equations are composed of the Navier-Stokes equations for the fluid, coupled to Newton's laws for the solids. Since we consider the case in which the fluid-solid systems fills a bounded domain we have to tackle a free boundary value problem. The main theoretical result in the paper asserts the global existence and uniqueness (up to possible contacts) of strong solutions of this problem. The second novelty brought in by this work is that we give a numerical method for the fluid-solid system. This method allows the simulation of the simultaneous displacement of several swimmers and it is tested on several examples.
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