Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs
description
Transcript of Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs
Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs
Peter Wittwer Département de Physique ThéoriqueUniversité de Genève
reading:
R. P. Feynman, Vol. II
G. K. Batchelor, An Introduction to Fluid Mechanics
L. Landau, E. Lifchitz, Mécanique des fluides
M. Van Dyke, An Album of Fluid Motion
collaborations:
Guillaume Van Baalen
Frédéric Haldi
Sebastian Bönisch
Vincent Heuveline
─ Introduction to the problem ─ Asymptotic analysis
─ Applications
Exterior Flows
Navier-Stokes
Re=0.16
Re=1.54
Re=56.5
Re=118
Re=7000
Case of finite volume
Case of infinite volume, I
Case of infinite volume, II
Asymptotic analysis
Results (d=2)
Interpretation:
Results (d=3)
Two steps:
─ construct downstream asymptotics
dynamical system invariant manifold theory renormalization group universality
─ determines asymptotics everywhere
Vorticity:
Vorticity equation
Fourier transform
Diagonalize
Stable and unstable modes
use contraction mapping principle
Large time asymptotics:
Two steps:
─ construct downstream asymptotics
dynamical system invariant manifold theory renormalization group universality
─ determines asymptotics everywhere
Determines asymptotics everywhere:
Applications
in collaboration with:
Sebastian BönischRolf Rannacher
Vincent Heuveline
Heidelberg & Karlsruhe
Adaptive boundary conditions
To second order:
Comparison with Experiment:
Cloud Microphysics and Climate
M. B. Baker, SCIENCE, Vol. 276, 1997
Work in progress:• d=2 case with lift (numerical)
• d=2 second order asymptotics (theory)
• d=3 (numerical)
• d=2, 3: free fall problem (numerical)
• d=3 case with rotation at infinity (theory; see P. Galdi
(2005) for recent results)
Other research groups:
• d=2 time periodic (theory)
Large time asymptotics: