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- LUC MIEUSSENS
- 2002

We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and… (More)

- Mounir Bennoune, Mohammed Lemou, Luc Mieussens
- J. Comput. Physics
- 2008

In this paper we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier-Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and… (More)

- Mohammed Lemou, Luc Mieussens
- SIAM J. Scientific Computing
- 2008

We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and non-equilibrium parts. We also use a projection technique that allows to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the… (More)

We present new numerical models for computing transitional or rarefied gas flows as described by the Boltzmann-BGK and BGK-ES equations. We first propose a new discrete-velocity model, based on the entropy minimization principle. This model satisfies the conservation laws and the entropy dissipation. Moreover, the problem of conservation and entropy for… (More)

- Pierre Degond, Jian-Guo Liu, Luc Mieussens
- Multiscale Modeling & Simulation
- 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… (More)

- Pierre Degond, Giacomo Dimarco, Luc Mieussens
- J. Comput. Physics
- 2010

This paper collects the efforts done in our previous works [8],[11],[10] to build a robust multiscale kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model… (More)

- Jian-Guo Liu, Luc Mieussens
- SIAM J. Numerical Analysis
- 2010

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334–368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied… (More)

- Pierre Degond, Giacomo Dimarco, Luc Mieussens
- J. Comput. Physics
- 2007

This paper is a continuation of earlier work [6] in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale. The basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations… (More)

- Luc Mieussens
- J. Comput. Physics
- 2013

The unified gas kinetic scheme (UGKS) of K. Xu et al. [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP)… (More)

This paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting… (More)