A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.
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June 2013
Research Article|
June 28 2013
A Fokker–Planck based kinetic model for diatomic rarefied gas flows
M. Hossein Gorji;
M. Hossein Gorji
a)
Institute of Fluid Dynamics
, ETH Zentrum, Sonneggstrasse 3, 8092 Zürich, Switzerland
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Patrick Jenny
Patrick Jenny
Institute of Fluid Dynamics
, ETH Zentrum, Sonneggstrasse 3, 8092 Zürich, Switzerland
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a)
Email: [email protected]
Physics of Fluids 25, 062002 (2013)
Article history
Received:
January 18 2013
Accepted:
May 06 2013
Citation
M. Hossein Gorji, Patrick Jenny; A Fokker–Planck based kinetic model for diatomic rarefied gas flows. Physics of Fluids 1 June 2013; 25 (6): 062002. https://doi.org/10.1063/1.4811399
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