1. Comparative Study Between Cubic and Ellipsoidal Fokker–Planck Kinetic Models
- Author
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M. Hossein Gorji, M. Pfeiffer, Eunji Jun, Luc Mieussens, Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Physics ,Aerospace Engineering ,Non-equilibrium thermodynamics ,Kinetic energy ,01 natural sciences ,Boltzmann equation ,Ellipsoid ,010305 fluids & plasmas ,010101 applied mathematics ,Physics::Popular Physics ,Entropy (classical thermodynamics) ,0103 physical sciences ,Particle ,Fokker–Planck equation ,Direct simulation Monte Carlo ,Statistical physics ,0101 mathematics ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; Motivated by improving the performance of particle based Monte-Carlo simulations in the transitional regime, Fokker-Planck kinetic models have been devised and studied as approximations of the Boltzmann collision operator. By generalizing the linear drift model, the cubic Fokker-Planck (cubic-FP) and ellipsoidal Fokker-Planck (ES-FP) have been proposed, in order to obtain the correct Prandtl number of 2/3 for a dilute monatomic gas. This study provides a close comparison between both models in low Mach and supersonic settings. While direct simulation Monte-Carlo (DSMC) here serves as the benchmark, overall close performance between cubic-FP, ES-FP and DSMC are observed. Furthermore, while the ES-FP out-performes the cubic-FP model in the shock region of the supersonic flow around a cylinder, the latter shows a better accuracy in the near continuum regime. It is argued that the reason behind these discrepancies lies in the entropy law besides the transport properties.
- Published
- 2019
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