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In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann equation based under minimization problem of the entropy under moments constraints [7], [11]. In particular the moment constraints and corresponding coefficients are linked with the eigenfunctions and eigenvalues of the linearized collision operator through the… (More)

- Stephane Brull, Lorenzo Pareschi
- Appl. Math. Lett.
- 2006

Recently linear dissipative models of the Boltzmann equation have been introduced in [7, 5]. In this work, we consider the problem of constructing suitable hydrodynamic approximations for such models.

This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directions and does not require any specially adapted coordinate system. It is also designed to be equally accurate in the strongly and the mildly anisotropic cases. The method is… (More)

This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ǫ, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit ǫ→0 is demonstrated to be a… (More)

Abstract The aim of this article is to construct a BGK-type model for polyatomic gases which gives in the hydrodynamic limit the proper transport coefficient. Its construction relies upon a systematic procedure: minimizing Boltzmann entropy under suitable moments constraints ([20, 9]). The obtained model corresponds to the ellipsoidal statistical model… (More)

The aim of this paper is to compute viscous correction terms for the isothermal quantum Euler system of Degond, Gallego, Méhats (SIAM Multiscale Model Simul., 6, 2007). We derive this model by using a Chapman-Enskog expansion up to order 1. In a last part, we consider a situation where the flow is nearly irrotational in order to get a simplified model.

- Stephane Brull
- 2009

— We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal.… (More)

- Stephane Brull
- 2009

The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An L existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L compactness… (More)

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