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Advances in the development of the Fokker-Planck method for simulation of rarefied gases

Basov, Leo and Grabe, Martin (2022) Advances in the development of the Fokker-Planck method for simulation of rarefied gases. In: 23rd STAB/DGLR Symposium on New Results in Numerical and Experimental Fluid Mechanics. 23. STAB-DGLR-Symposium 2022, 09.-10. Nov. 2022, Berlin, Germany.

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Official URL: https://www.tu.berlin/index.php?id=27890


Flows encountered in space applications, like atmospheric reentry or jet plume interactions, are characterized by a wide range of the Knudsen number. The well-known Boltzmann equation describes the evolution of a distribution function f in such rarefied flows due to intermolecular collisions: A common approach to numerically solve Eq. (1) is the Direct Simulation Monte-Carlo (DSMC) method pioneered by Bird [1]. The method is very efficient for high Knudsen numbers but becomes computationally intensive when approaching the continuum limit. Approximations of the collision operator S Boltz in Eq. (1) can greatly reduce this computational cost. One such approximation is the Fokker-Planck collision operator S FP [2]: where the drift coefficient A i and the diffusion coefficient D of Eq. (2) are model parameters chosen in such a way that moments calculated using the Boltzmann collision operator are reproduced in the continuum limit. The resulting Fokker-Planck equation can be solved through stochastic motion which in turn can be modelled using a particle method. Due to the similarity in their formulation a hybrid method based on DSMC and FP can be derived which allows the computationally efficient simulation of flows with a broad range of Knudsen numbers [3]. For the application of the FP model to engineering problems the simulation of complex gases and gas mixtures must be possible. The FP model has been extended from monatomic to diatomic gas for single species [4, 5] as well as for mixtures [6, 7]. However, the extension of the model to polyatomic gases for single and multispecies applications is still a research topic. This paper discusses how the recently developed FP models for diatomic gases can be extended to allow modeling of polyatomic molecules using the Master-equation ansatz. We further point out why the current multi-species formulations [6, 7] do not contain the special case of a single-species gas [8] and propose modifications to establish consistency.

Item URL in elib:https://elib.dlr.de/186895/
Document Type:Conference or Workshop Item (Speech)
Title:Advances in the development of the Fokker-Planck method for simulation of rarefied gases
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Basov, LeoUNSPECIFIEDhttps://orcid.org/0000-0003-4133-7876UNSPECIFIED
Grabe, MartinUNSPECIFIEDhttps://orcid.org/0000-0003-0361-2734UNSPECIFIED
Date:November 2022
Journal or Publication Title:23rd STAB/DGLR Symposium on New Results in Numerical and Experimental Fluid Mechanics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
EditorsEmailEditor's ORCID iDORCID Put Code
Keywords:Fokker-Planck, Boltzmann equation, rarefied flow, multi species
Event Title:23. STAB-DGLR-Symposium 2022
Event Location:Berlin, Germany
Event Type:international Conference
Event Dates:09.-10. Nov. 2022
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 - Reusable Space Systems and Propulsion Technology
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Spacecraft, GO
Deposited By: Basov, Leo
Deposited On:08 Dec 2022 21:35
Last Modified:29 Mar 2023 00:51

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