摘要:

We study the numerical approximation of solutions to a class of nonlinear kinetic equations for reacting gas mixtures. We first prove the existence and uniqueness of solutions and then provide a time-discretized version of the equations. We finally obtain a probabilistic-convergent, numerical scheme by extending simulation techniques for the solutions of the classical Boltzmann equation.

ISSN:0041-1450    

DOI:10.1080/00411459708020289

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We derive error estimates in certain weightedL2-norms for the streamline diffusion and discontinuous Galerkin finite element methods for steady state, energy dependent, Fermi and Fokker-Planck equations in two space dimensions, giving error bounds of order O(hk+1/2), for the weighted current functionJ, as in the convection dominated convection-diffusion problems, withJεHk+1(Ω) andhbeing the quasi-uniform mesh size in triangulation of our three dimensional phase-space domain Ω =Iz, × Iy× Iz, with z corresponding to the velocity variable. Our studies, in this paper, contain a priori error estimates for Fermi and Fokker-Planck equations with both piecewise continuous and piecewise discontinuous (inxandxy-directions) trial functions. The analyses are based on stability estimates which relay on an angular symmetry (not isotropy!) assumption. A continuation of this paper, the a posteriori error estimates for Fermi and Fokker-Planck equations, is the subject of a future work.

ISSN:0041-1450    

DOI:10.1080/00411459708020290

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We prove in this work that the solution of the two-dimensional spatially homogeneous Boltzmann equation with Maxwellian molecules lies “almost” inH1(in the velocity variable) as soon as the initial datum has finite mass, energy and entropy. No assumption of radial symmetry of the solution is made in this paper.

ISSN:0041-1450    

DOI:10.1080/00411459708020291

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We consider Discrete Boltzmann Models (DBMs) with two constraints: First, models with an arbitrary number of velocities and speeds and second, for the solutions with two asymptotic states, they will satisfy the mass ratio relation deduced from the continuous theory with two Maxwellian states. Consequently we restrict our study to travelling waves along anx-axis, with two asymptotic states (shock waves if the Lax Criterion is satisfied). We consider a class of models, called “nested s-squares”, with an arbitrary number s of squares and a rest particle. Our god is to obtain general results, and to seek whether scaling properties can exist when the number of velocities increases. In other words whether physical properties become invariant when the number of squares is sufficiently large. We build up macroscopic quantities consistent with both the conservation laws and the continuous theory relation. At one asymptotic state called (i), we consider isotropic solutions. At the other called (ii), we consider mainly two classes of solutions: Either the number of squares s is arbitrary while the number with nonzero densities is fixed (Class I) or both are varying with s (Class II). Equivalently either the momentum conservation law contains only macroscopic quantities or mixes macroscopic and microscopic quantities.

ISSN:0041-1450    

DOI:10.1080/00411459708020292

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We show, for a particular collision kernel, that the entropy tends to its equilibrium limit for all solutions of the spatially homogeneous Boltzmann equation with finite energy, finite entropy initial data. This verses the natural conjecture following from the BoltzmannH-theorem. All previous results in this direction placed additional restrictions on the initial data beyond the physical ones considered here.

ISSN:0041-1450    

DOI:10.1080/00411459708020293

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459708020294

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor