Multiresolution analysis of incompressible flows interaction with forced deformable bodies

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

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

In the present investigation, a space adaptive multiresolution method is developed to solve the incompressible two-dimensional Navier-Stokes equations in the vorticity-stream-function formulations including the penalization term. The new method is based on a multiresolution analysis which allows to reduce the number of active grid points significantly by refining the grid automatically via nonlinear thresholding of the wavelet coefficients in a one-to-one correspondence with the grid points. To study the accuracy of the method, dipole collision with a straight wall is considered as a benchmark, a good agreement between the results of adaptive simulations and that of uniform grid solver is obtained. The grid adaptation strategy uses an estimation of the local regularity of the solution via wavelet coefficients at a given time step. An extension to interactions with forced deformable bodies, i.e., swimming of a fish, is done using the volume penalization method. 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. The results of swimming fish are compared with those of Gazzola et al. where a uniform grid is used. The obtained results show that the CPU-time of the adaptive simulations can be significantly reduced with respect to simulations on a regular grid. Nevertheless the accuracy order of the underlying numerical scheme is preserved.

Mots clés: Incompressible unsteady flow; Vorticity-stream-function formulation; Penalization method; Fish swimming; Point value multiresolution analysis

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

Seyed Amin Ghaffari, Kai Schneider, Stéphane Viazzo, Patrick Bontoux. Multiresolution analysis of incompressible flows interaction with forced deformable bodies. 11th World Congress on Computational Mechanics, ECFD IV, Jul 2014, Barcelona, Spain. pp.5002-5013. ⟨hal-01063359⟩