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A kinetic Fokker-Planck approach to model hard-sphere gas mixtures

Hepp, Christian and Grabe, Martin and Hannemann, Klaus (2020) A kinetic Fokker-Planck approach to model hard-sphere gas mixtures. Physics of Fluids, 32 (2), pp. 1-18. American Institute of Physics (AIP). doi: 10.1063/1.5141909. ISSN 1070-6631.

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Official URL: https://aip.scitation.org/doi/abs/10.1063/1.5141909


Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker-Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad's 13 moment equations on a Navier-Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He-Ar mixture.

Item URL in elib:https://elib.dlr.de/138579/
Document Type:Article
Title:A kinetic Fokker-Planck approach to model hard-sphere gas mixtures
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hepp, ChristianUNSPECIFIEDhttps://orcid.org/0000-0001-8465-9926UNSPECIFIED
Grabe, MartinUNSPECIFIEDhttps://orcid.org/0000-0003-0361-2734UNSPECIFIED
Hannemann, KlausUNSPECIFIEDhttps://orcid.org/0000-0002-9653-4087UNSPECIFIED
Date:18 February 2020
Journal or Publication Title:Physics of Fluids
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 1-18
EditorsEmailEditor's ORCID iDORCID Put Code
Publisher:American Institute of Physics (AIP)
Keywords:Kinetic particle method, Fokker-Planck equation, None equilibrium flows, Multi species flow, DSMC
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transportation
DLR - Research area:Raumfahrt
DLR - Program:R RP - Space Transportation
DLR - Research theme (Project):R - Wiederverwendbare Raumfahrtsysteme (old)
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Spacecraft, GO
Deposited By: Grabe, Dr. Martin
Deposited On:15 Dec 2020 23:01
Last Modified:24 Oct 2023 11:13

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