Papers by jacques schneider
Communications in Mathematical Sciences, 2015
We aim to present a relaxation model that can be used in real simulations of dilute multicomponen... more We aim to present a relaxation model that can be used in real simulations of dilute multicomponent reacting gases. The kinetic framework is the semi-classical approach with only one variable for the internal energy modes. The relaxation times for the internal energy modes are assumed to be smaller than the chemistry characteristic times. The strategy is the same than in [10]. That is a sum of operators for respectively the mechanical and chemical processes. The mechanical operator(s) is the "natural" extension to polyatomic gases of the method of moment relaxations presented in [8] [11]. The derivation of the chemical model lies on the chemical processes at thermal equilibria. It is shown that this BGK approach features the same properties as the Boltzmann equation: conservations and entropy production. Moreover null entropy production states are characterized by vanishing chemical production rates. We also study the hydrodynamic limit in the slow chemistry regime. Finally we show that the whole set of parameters that are used in the derivation of the model can be calculated by softwares such as EGlib [17] or STANJAN [36].
While the Web makes an increasing number of ontologies widely available for applications, how to ... more While the Web makes an increasing number of ontologies widely available for applications, how to discover ontologies becomes a more challenging issue. Existing approaches are mainly based on keywords and metadata information of ontologies, rather than semantic entailments of ontologies. In this paper, we present an ontology search engine, ONTOSEARCH2, which provides three approaches to searching ontologies semantically. These approaches take advantage of ON-TOSEARCH2's efficient query answering capability.
Le developpement de projets de vehicules spatiaux inclut la comprehension de la dynamique des gaz... more Le developpement de projets de vehicules spatiaux inclut la comprehension de la dynamique des gaz rarefies. Cette mecanique est decrite par l'equation de boltzmann. A l'heure actuelle, la majeure partie des methodes numeriques pour resoudre cette equation sont de type probabiliste. Les progres dans le domaine de l'informatique, et notamment dans les calculateurs paralleles ouvrent la porte a une approche plus directe. Nous proposons un algorithme deterministe de resolution dont le but est de pallier aux inconvenients des methodes monte-carlo. Nous decrivons successivement une methode de differences finies pour le probleme homogene et de volumes finis pour le transport. Le schema general est implemente sur un hypercube
This paper is devoted to the construction of a BGK operator for gas mixtures. The construction is... more This paper is devoted to the construction of a BGK operator for gas mixtures. The construction is based as in ([12], [13]) on the introduction of relaxation coefficients and a principle of minimization of the entropy under constraints of moments. These free parameters are compared with the free parameters introduced in the Thermodynamics of Irreversible Processes approach of the Navier-Stokes system. At the end the BGK model is proved to satisfy Fick and Newton laws.
Communications in Mathematical Sciences, 2014
Lecture Notes in Physics
ABSTRACT
We prove the convergence of finite-difference approximations to solutions of the Boltzmann equati... more We prove the convergence of finite-difference approximations to solutions of the Boltzmann equation. An essential step is the proof of convergence of discrete approximations to the collision integral. This proof relies on our previous results on the consistency of this approximation. For the space-homogeneous problem we prove strong convergence of our discrete approximation to the strong solution of the Boltzmann equation. In the space-dependent case we prove weak convergence to DiPerna-Lions solutions.
ABSTRACT We present a new relaxation model for gas mixtures introduced in a previous paper. This ... more ABSTRACT We present a new relaxation model for gas mixtures introduced in a previous paper. This model is able to fit transport coefficients of the true Navier-Stokes equations given by the hydrodynamical limit of the Boltzmann equation(s). Here the same hydrodynamical limit is obtained by introducing relaxation coefficients on certain moments of the distribution functions. Next the whole model is set by using entropy minimization under moments constraints. In the present case the BGK operator allows to recover the exact Fick and Newton laws and satisfy the classical fundamental properties of the Boltzmann equations for inert gas mixtures.
Transport Theory and Statistical Physics, 1994
A numerical method for solving the Boltzmann equation is proposed. This method is based on a fini... more A numerical method for solving the Boltzmann equation is proposed. This method is based on a finite difference scheme for the approximation of the collision kernel and a finite element scheme for the transport phase. The properties of the Boltzmann equation also are also satisfied in our method.
Transport Theory and Statistical Physics, 1996
SIAM Journal on Numerical Analysis, 1997
ANDRZEJ PALCZEWSKIt, JACQUES SCHNEIDERt, AND ALEXANDRE V. BOBYLEV? Abstract. In this paper, we st... more ANDRZEJ PALCZEWSKIt, JACQUES SCHNEIDERt, AND ALEXANDRE V. BOBYLEV? Abstract. In this paper, we study the link between a certain class of discrete-velocity models (DVMs) and the Boltzmann equation. Those models possess an infinite number of ...
International Journal for Numerical Methods in Fluids, 2006
European Journal of Mechanics - B/Fluids, 2012
ESAIM: Mathematical Modelling and Numerical Analysis, 2004
Approximation theory in the context of probability density function turns out to go beyond the cl... more Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021-1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global existence theorem for such an approximation and derive as a by-product a necessary and sufficient condition for the so-called problem of moment realizability. Applications of the above result are given in kinetic theory: first in the context of Levermore's approach and second to design generalized BGK models for Maxwellian molecules.
Continuum Mechanics and Thermodynamics, 2009
The aim of this article is to construct a BGK-type model for polyatomic gases which gives in the ... more 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 introduced in [2]. We also study the return to equilibrium of its solutions in the homogeneous case.
Continuum Mechanics and Thermodynamics, 2008
In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann e... more 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 Chapman-Enskog expansion. Then we deduce from this expansion a single relaxation term of BGK-type. Here we stop the moments constraints at the order 2 in the velocity v and recover the Ellipsoidal Statistical model [8].
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
… DES SCIENCES PARIS …, 1995
ABSTRACT We present a result of consistency of a discrete velocity model with the Boltzmann equat... more ABSTRACT We present a result of consistency of a discrete velocity model with the Boltzmann equation. This model is constructed as a quadrature formula of the collision integral, by using a regular grid in the velocity space ℝ 3 . The convergence of the above approximation leans mainly on some property of uniform repartition of integer roots of the equation p 2 +q 2 +r 2 =n, where n is an integer.
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Papers by jacques schneider