Oberseminar Numerische Mathematik / Scientific Computing
Romain Nguyen van Yen
LMD-IPSL-CNRS, Ecole Normale Superieure, Paris
Dissipative structures in the inviscid limit of the 2D Navier-Stokes equations with no-slip boundary conditions
Abstract:
The behavior of solutions to the Navier-Stokes equations with no-slip boundary conditions when the viscosity goes to zero has been a long standing mathematical problem since its formulation by Prandtl. The main difficulty lies in the possible production of extreme velocity gradients near boundaries. After reviewing a few important theorems, we present results of new numerical experiments with a maximum Reynolds numbers of order 104, that is accessible by taking into account up to 109222 Fourier modes, along with a volume penalization method to impose the no-slip condition. These results support a scenario in which the energy dissipation rate remains strictly positive in the inviscid limit. A wavelet analysis of the vorticity field suggests that this energy dissipation is due to the prominence of "dissipative structures" detaching from the boundary. Some implications for modeling of boundary layer detachment phenomena are briefly discussed.
| Datum: | 01.02.10 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |