See the published version of this preprint at Advances in Aerodynamics.
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Lianping Wang
Southern University of Science and Technology
Corresponding Author
ORCiD: https://orcid.org/0000-0003-4276-0051
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In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.
Keywords
Mesoscopic CFD methods, Boltzmann equation, inverse design, the Navier-Stokes-Fourier system, Chapman-Enskog analysis, structure of distribution function, thermal forcing, boundary condition, bulk viscosity, Prandtl number
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View the published article at Advances in Aerodynamics.
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Editorial decision: Major revision
On 26 Oct, 2020
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Received 29 Sep, 2020
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Reviewer #3 agreed
On 02 Sep, 2020
Review #1 received
Received 02 Sep, 2020
Reviewer #2 agreed
On 01 Sep, 2020
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Reviewer #1 agreed
On 31 Aug, 2020
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On 27 Aug, 2020
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On 26 Aug, 2020
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On 26 Aug, 2020
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A new preprint design is coming!
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See the published version of this preprint at Advances in Aerodynamics.
This is a preprint, a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research
Lianping Wang
Southern University of Science and Technology
Corresponding Author
ORCiD: https://orcid.org/0000-0003-4276-0051
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Published
View the published article at Advances in Aerodynamics.
Version 1
Posted 01 Sep, 2020
No community comments so far
Editorial decision: Major revision
On 26 Oct, 2020
Review #3 received
Received 29 Sep, 2020
Review #2 received
Received 28 Sep, 2020
Reviewer #3 agreed
On 02 Sep, 2020
Review #1 received
Received 02 Sep, 2020
Reviewer #2 agreed
On 01 Sep, 2020
Reviewers invited
Invitations sent on 31 Aug, 2020
Reviewer #1 agreed
On 31 Aug, 2020
Editor assigned
On 27 Aug, 2020
Submission checks complete
On 26 Aug, 2020
Editor invited
On 26 Aug, 2020
First submitted
On 24 Aug, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Aeronautics and Astronautics
License:
This work is licensed under a CC BY 4.0 License. Read Full License
View the published article at Advances in Aerodynamics.
In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.
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