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 |