Math @ Duke

Publications [#246901] of JianGuo Liu
Papers Published
 Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects,
Multiscale Modeling & Simulation, vol. 5 no. 3
(September, 2006),
pp. 940979, Society for Industrial & Applied Mathematics (SIAM), ISSN 15403459 [doi]
(last updated on 2019/06/17)
Abstract: 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.
Keywords: KineticFluid coupling, Kinetic equation, Hydrodynamic approximation, Diffusion approximation


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