Wavelet methods in computational fluid dynamics

Kai Schneider (1, 2) , Oleg V. Vasilyev (3)

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
2 CMI - Centre de Mathématiques et Informatique [Marseille]
3 Department of Mechanical Engineering

This article reviews state-of-the-art adaptive, multiresolution wavelet methodologies for modeling and simulation of turbulent flows with various examples. Different numerical methods for solving the Navier-Stokes equations in adaptive wavelet bases are described. We summarize coherent vortex extraction methodologies, which utilize the efficient wavelet decomposition of turbulent flows into space-scale contributions, and present a hierarchy of wavelet-based turbulence models. Perspectives for modeling and computing industrially relevant flows are also given.

Mots clés: multiresolution analysis; adaptive methods for Navier-Stokes equations; hierarchy of turbulence models; coherent vortex extraction and simulation; adaptive large-eddy simulations

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

Kai Schneider, Oleg V. Vasilyev. Wavelet methods in computational fluid dynamics. Annual Review of Fluid Mechanics, 2010, 42, pp.473-503. ⟨10.1146/annurev-fluid-121108-145637⟩. ⟨hal-01024632⟩