patrick jenny manuel torrilhon stefan heinzmaths.dur.ac.uk/lms/091/talks/jenny2.pdf · patrick...
TRANSCRIPT
![Page 1: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/1.jpg)
Institute of Fluid DynamicsInstitute of Fluid Dynamics
Patrick Jenny (IFD, ETH Zürich)
Manuel Torrilhon (SAM, ETH Zürich)
Stefan Heinz (Dept. of Mathematics, University of Wyoming)
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Institute of Fluid Dynamics
Fokker Planck Equation for PDF Evolution
![Page 3: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/3.jpg)
Institute of Fluid DynamicsPatrick Jenny
• Kinetic Description of Non-Equilibrium G as
• Consistency with Continuum Fluid Dynamics
• Collision Models
• Fokker Planck Model and Integration Scheme
• Knudsen Paradox
• Performance
• Conclusion
Outline
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Institute of Fluid DynamicsPatrick Jenny
Kinetic Description of Non-Equilibrium Gas
Assume that the statistics of particles in a monatomic gas can be described by the mass density function
with the weights
In equilibrium, the velocity PDF is given by the Maxwell distribution:
![Page 5: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/5.jpg)
Institute of Fluid DynamicsPatrick Jenny
Consistency with Fluid Dynam ics
with the weights
![Page 6: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/6.jpg)
Institute of Fluid DynamicsPatrick Jenny
Consistency with Fluid Dynam ics
with the weights
![Page 7: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/7.jpg)
Institute of Fluid DynamicsPatrick Jenny
Consistency with Fluid Dynam ics
with the weights
![Page 8: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/8.jpg)
Institute of Fluid DynamicsPatrick Jenny
Consistency with Fluid Dynam ics
with the weights
Chapman-Enskog Expansion => Navier-Stokes
![Page 9: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/9.jpg)
Institute of Fluid DynamicsPatrick Jenny
Collision Models
with the weights
![Page 10: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/10.jpg)
Institute of Fluid DynamicsPatrick Jenny
with the weights
Collision Models
![Page 11: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/11.jpg)
Institute of Fluid DynamicsPatrick Jenny
with the weights
Here we propose a Fokker-Planck operator:
motivation: leads to the possibility to use highly efficient numerical methods
Collision Models
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Institute of Fluid DynamicsPatrick Jenny
Collision Models
![Page 13: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/13.jpg)
Institute of Fluid DynamicsPatrick Jenny
Fokker-Planck Solution Algorithm
![Page 14: Patrick Jenny Manuel Torrilhon Stefan Heinzmaths.dur.ac.uk/lms/091/Talks/jenny2.pdf · Patrick Jenny Institute of Fluid Dynamics Kinetic Description of Non-Equilibrium Gas Assume](https://reader036.vdocuments.site/reader036/viewer/2022090603/6056b1bebec041070051b4a7/html5/thumbnails/14.jpg)
Institute of Fluid DynamicsPatrick Jenny
Fokker-Planck Solution Algorithm