摘要:

This paper deals with the 2 particle Boltzmann collision operator in axisymmetric geometry. We derive a reduced expression of the collision operator for axisymmetric distribution functions. The purpose is to give an explicit expression which can be suitable for numerical computations.

ISSN:0041-1450    

DOI:10.1080/00411458908204319

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We present a new two-grid method for solution of matrix H-equations that is a generalization of a method due to Atkinson. Our new algorithm provides mesh independent q-linear convergence and can be accelerated to a superlinearly convergent algorithm by means of a quasi-Newton method. In addition the algorithm requires far less storage than Newton's method. Such considerations are especially important for the large problems generated by discretizations of H-equations for matrix-valued functions. Such equations arise in radiative transfer, polarization, and multi-group neutron transport. As a numerical example we show measured convergence rates and discuss timings for a matrix H-equation arising in radiative transfer.

ISSN:0041-1450    

DOI:10.1080/00411458908204320

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness).

ISSN:0041-1450    

DOI:10.1080/00411458908204321

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Entropy profiles in the shock wave solutions of discrete velocity models of the Boltzmann equation are studied. Overshoot of the local entropy in the interior of the shock wave and dependence of the solutions on the Maxwellian limit conditions are discussed.

ISSN:0041-1450    

DOI:10.1080/00411458908204322

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

New estimations of the nonlinear Boltzmann collision operatorJ(F) are given, which include all known estimations ofJ(F) in sup-norm. These new estimations are used to prove the existence of a mild solution to the nonlinear Boltzmann equation both inR3and in the case of the flow past a body inR3. The solution is global in time if the initial data decay fast enough at infinity and satisfy a smallness condition. Furthermore, the existence theorem admits solutions that are unbounded both in the space variable and the velocity variable. Examples are given in which it is shown that the smallness condition can be realized either through the smallness of supnorm of the initial datum or through the smallness of the support of the initial datum with respect toxorvvariables. The last condition, physically speaking, corresponds to an initial datum that represents a small cloud of gas, or an arbitrary cloud of gas whose particle velocities are sufficiently close to some vo ε R3.

ISSN:0041-1450    

DOI:10.1080/00411458908204323

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A Review of Speakable and Unspeakable in Quantum Mechanics By J. S. Bell, Cambridge University Press, Cambridge and New York (1987), xii + 212 pp., $44.50 (hard), $14.95 (paper).

ISSN:0041-1450    

DOI:10.1080/00411458908204324

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor