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Macroscopic fluid models with localized kinetic upscaling effects

Publication ,  Journal Article
Degond, P; Liu, JG; Mieussens, L
Published in: Multiscale Modeling and Simulation
September 1, 2006

This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the nonequilibrium part of the distribution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretize our models, and several numerical examples are used to validate the method. © 2006 Society for Industrial and Applied Mathematics.

Duke Scholars

Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

September 1, 2006

Volume

5

Issue

3

Start / End Page

940 / 979

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
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Degond, P., Liu, J. G., & Mieussens, L. (2006). Macroscopic fluid models with localized kinetic upscaling effects. Multiscale Modeling and Simulation, 5(3), 940–979. https://doi.org/10.1137/060651574
Degond, P., J. G. Liu, and L. Mieussens. “Macroscopic fluid models with localized kinetic upscaling effects.” Multiscale Modeling and Simulation 5, no. 3 (September 1, 2006): 940–79. https://doi.org/10.1137/060651574.
Degond P, Liu JG, Mieussens L. Macroscopic fluid models with localized kinetic upscaling effects. Multiscale Modeling and Simulation. 2006 Sep 1;5(3):940–79.
Degond, P., et al. “Macroscopic fluid models with localized kinetic upscaling effects.” Multiscale Modeling and Simulation, vol. 5, no. 3, Sept. 2006, pp. 940–79. Scopus, doi:10.1137/060651574.
Degond P, Liu JG, Mieussens L. Macroscopic fluid models with localized kinetic upscaling effects. Multiscale Modeling and Simulation. 2006 Sep 1;5(3):940–979.

Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

September 1, 2006

Volume

5

Issue

3

Start / End Page

940 / 979

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics