摘要:

Interaction integrals Vℓvarise naturally in so-called moment theories of solution of Boltzmanns equation in which the velocity distribution function is represented by an expansion in Burnett functions. They are essentially matrix elements of scattering cross sections with respect to Sonine polynomials. In this paper, we discuss firstly the way in which the Vℓvarise in the test particle problem when representing the linear Boltzmann collision operator in the Burnett function basis with two free parameters, temperature and drift velocity respectively. Secondly, properties of Vℓvare discussed, recurrence relationships derived and both analytic and numerical evaluation is carried out for both elastic and inelastic processes, described by various model and realistic cross sections. Finally, the significance of these results for transport coefficient calculation is briefly discussed.

ISSN:0041-1450    

DOI:10.1080/00411458508211678

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The existence of strict solutions to the initial value problem for the Boltzmann equation with force term is investigated. For a certain class of velocity dependent external forces compatible with equilibrium, and for Gra[dacute]s generalized hard molecular potentials, the global existence, uniqueness, positivity and approach to equilibrium of solutions to the spatially homogeneous Boltzmann equation is proved in the case of initial data close to equilibrium (in the sense that the first moments are those of the equilibrium solution and a certain norm of the deviation from equilibrium is small). A local existence theorem is stated in the spatially inhomogeneous case, both for Gradcar;s hard and soft intermolecular potentials. One of the main steps of the argument concerning the nonlinear part of the theory, is formalized in an abstract theorem of possible independent interest.

ISSN:0041-1450    

DOI:10.1080/00411458508211679

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The one-dimensional transport equation in slab geometry with periodic boundary conditions is studied. It reduces to the integral equation of the Peierls type. The spectral radius of the integral operator is estimated. We analyze the discrete-ordinates algorithm for estimating the solution. Convergence is proved and methods of estimating the rate of convergence are described. The estimates of some quadrature rules are derived by way of an example. The numerical results confirm the convergence properties of the proposed algorithm.

ISSN:0041-1450    

DOI:10.1080/00411458508211680

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this paper, we prove the convergence of the iteration scheme of the discrete ordinates method for the plane geometry transport equation discretised using positive weighted diamond schemes. General anisotropic scattering, boundary conditions and cross-sections are included. For the case of isotropic scattering and vacuum boundary conditions, the eigenvalues of the iteration matrix are shown to be real.

ISSN:0041-1450    

DOI:10.1080/00411458508211681

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The critical problem for a finite slab with sinusoidally space-dependent scattering ratio is discussed. Numerical results for the corresponding critical parameter are reported and commented.

ISSN:0041-1450    

DOI:10.1080/00411458508211682

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

by roger peyret and thomas d, taylor, springer, 1983, x + 358 pp., $42.50.

ISSN:0041-1450    

DOI:10.1080/00411458508211683

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor