A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion

Journal Article · Sat Feb 20 04:00:00 EST 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.10.008· OSTI ID:21333928

Jenny, Patrick ^[1]; Torrilhon, Manuel ^[2]; Heinz, Stefan ^[3]

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1. Institute of Fluid Dynamics, ETH Zurich, Sonneggstrasse 3, CH-8092 Zurich (Switzerland)
2. Seminar for Applied Mathematics, ETH Zurich, Raemistrasse 101, CH-8092 Zurich (Switzerland)
3. Department of Mathematics, University of Wyoming, 1000 East University Avenue, Laramie, WY 82071 (United States)

In this paper, 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. The application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages. Moreover, results of a test case with geometrically complex boundaries are presented.

• OSTI ID: 21333928
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 4 Vol. 229; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
BOLTZMANN EQUATION
FOKKER-PLANCK EQUATION
MATHEMATICAL SOLUTIONS
MOLECULAR DYNAMICS METHOD
MONTE CARLO METHOD
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
SIMULATION
STOCHASTIC PROCESSES