Publications [#246901] of Jian-Guo Liu

Papers Published

1. Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling and Simulation, vol. 5 no. 3 (September, 2006), pp. 940-979, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459 [doi]
   (last updated on 2025/05/01)

   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:
   Kinetic-Fluid coupling, Kinetic equation, Hydrodynamic approximation, Diffusion approximation