An efficient algorithm for simulation of forced deformable bodies interacting with incompressible flows; Application to fish swimming

Patrick Bontoux (1) , Stéphane Viazzo (1) , Kai Schneider (1) , Seyed Amin Ghaffari (1)

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible flows. The temporal and spatial discretizations of the Navier-Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge-Kutta and compact finite differences. By using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the solution of the Poisson equation to ensure the incompressibility constraint down to machine zero. For introducing a deformable body in fluid flow, an immersed boundary method is applied to the solution of the Navier-Stokes equations as a forcing term. A Lagrangian structure grid with prescribed motion cover the deformable body interacting with surrounding fluid due to hydrodynamic forces and moment calculated on an Eulerian reference Cartesian grid. An efficient law for curvature control of an anguilliform fish, swimming to a prescribed goal, is proposed. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming control and also for a variety of fluid/solid interaction problems.

Mots clés: Fluid interaction with forced deformable bodies; Compact fourth-order direct Poisson solver; Volume penalization; Fish swimming/turning

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Patrick Bontoux, Stéphane Viazzo, Kai Schneider, Seyed Amin Ghaffari. An efficient algorithm for simulation of forced deformable bodies interacting with incompressible flows; Application to fish swimming. 11th World Congress on Computational Mechanics, ECCM V, Jul 2014, Barcelona, Spain. pp.787-798. ⟨hal-01063358⟩