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Oberseminar Numerische Mathematik / Scientific Computing

 

Patrick Jenny

Institute of Fluid Dynamics, ETHZ Zürich

A Solution Algorithm for the Fluid Dynamic Equations Based on a Stochastic Model for Molecular Motion

Abstract:

A stochastic model is presented to simulate the flow of gases, which are not in thermodynamic equilibrium, like in rarefied or micro situations. For the interaction of a particle with others, statistical moments of the local ensemble have to be evaluated, but unlike in molecular dynamics simulations or DSMC, no collisions between computational particles are considered. In addition, a novel integration technique allows for time steps independent of the stochastic time scale. The stochastic model represents a Fokker-Planck equation in the kinetic description, which can be viewed as an approximation to the Boltzmann equation. This allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations. The fluid dynamic equations of Navier-Stokes and Fourier are fully recovered for small relaxation times, while for larger values the new model extents into the kinetic regime.

Numerical studies demonstrate that the stochastic model is consistent with Navier-Stokes in that limit, but also that the results become significantly different, if the conditions for equilibrium are invalid. As a quantitative example it is shown that the mass flow rate through a channel is correctly predicted as a function of the Knudsen number. Moreover, results of a test case with geometrically complex boundaries are presented.

Datum: 07.12.09
Zeit:17:00 Uhr
Ort:FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin.
Raum:Raum 032, Erdgeschoss

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