No-slip and Free-slip divergence-free wavelets in three and higher dimension for the simulation of incompressible viscous flows

Souleymane Kadri (1) , Valérie Perrier (2)

1 ULR - La Rochelle Université
2 CVGI - Calcul des Variations, Géométrie, Image

This work concerns divergence-free wavelet based methods for the numerical resolution of Navier-Stokes equations. It generalizes to higher dimension the approach of [23] that reformulates the projection method using the Helmholtz-Hodge decomposition in wavelet domain. The solution is searched in a finite dimensional free-slip divergence-free wavelet space, with time-dependent wavelet coefficients. We prove and verify the convergence of a first-order time numerical scheme for the Helmholtz-Hodge based projection method. Numerical simulations on the 3D Lid driven cavity flow show the accuracy and efficiency of the method.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Souleymane Kadri, Valérie Perrier. No-slip and Free-slip divergence-free wavelets in three and higher dimension for the simulation of incompressible viscous flows. R. Deiterding; M.-O. Domingues; K. Schneider. Cartesian CFD Methods for Complex Applications, Springer, 2021, 978-3-030-61760-8. ⟨10.1007/978-3-030-61761-5_3⟩. ⟨hal-02555973⟩