摘要:

Two Hermite based spectral methods are examined. A method based on an asymmetric expansion in Hermite polynomials offers theoretical advantages over other spectral basis sets for the treatment of the velocity variables in the Vlasov-Maxwell equations of plasma kinetic theory. It provides for exact conservation of energy, momentum, and particles (in a fully discrete system, not just as the discretization is refined), and this conservation is not effected by the use of velocity space filters during time-stepping. The asymmetric Hermite method exactly solves the spatially uniform problem (plasma oscillations), and both Hermite based methods exactly recover the temporal behavior of retained moments for free streaming in a periodic system. Yet the cost of these Hermite methods scales only linearly with the number of degrees for freedom, just like a finite difference method, and in fact the number of runtime operations required per degree of freedom in the asymmetric method can be essentially identical to a central difference in velocity. The numerical results presented here demonstrate that for the linearized Vlasov equation the asymmetric Hermite method can offer many orders of magnitude greater accuracy in eigenvalue calculations than finite difference methods and can also yield greater accuracy than symmetric Hermite methods.

ISSN:0041-1450    

DOI:10.1080/00411459608204828

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We propose a conservative and entropic discrete-velocity method to compute the solutions of the Boltzmann equation in the case of monoatomic species. We begin by defining a discrete collision kernel on a velocity lattice verifies all the properties of the continuous kernel. The continuous Boltzmann equation will be replaced by a Boltzmann equation for a discrete velocity gas, which is a hyperbolic system. This equation will be discretize by a finite volume scheme. For the evaluation of the collision term we use acceleration procedures of Monte Carlo type. The possibilities of our scheme will be illustrate by numerical tests in 1 and 2 space dimensions.

ISSN:0041-1450    

DOI:10.1080/00411459608204829

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A new numerical nodal method is developed for multigroup slab-geometry discrete ordinates (SN) eigenvalue problems with no spatial truncation error. The numerical results are exactly those of the dominant analytical solution of the multigroup SNeigenvalue problem on the grid points apart from finite arithmetic considerations and regardless of the spatial grid. We have implemented the option of using the multigroup albedo boundary condition, that is a measure of the reflective power of the neutron reflector, e.g., water or graphite. The Power method used in the outer iterations for convergence of the dominant numerical solution has been accelerated by a scheme based on Tchebycheff extrapolation of the fission source. Numerical results are given to illustrate the method's accuracy.

ISSN:0041-1450    

DOI:10.1080/00411459608204830

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We consider time-dependent photon transport in an interstellar cloud V, containing one or more clumps whose centers are randomly distributed within V. For simplicity, we assume that V occupies the slab {s: -R<s<R}. However, most of the results still hold if V is a given three-dimensional convex region. The physical system is first written as two coupled evolution problems in suitable Banach spaces. Then, the techniques of semigroup theory are used to prove existence and uniqueness of a positive solution. Finally, some approximate solutions arc discussed.

ISSN:0041-1450    

DOI:10.1080/00411459608204831

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This paper is devoted to investigating particle transport in nonhomogeneous bounded media with [0,vM] energy and anisotropic scattering-fission kernel. The time-dependent equation and the corresponding transport operatorAare discussed in the space of continuous functions. Some aspects of the spectral properties ofA(e.g., the properties of Pas(A) and the dominant eigenvalue ofA, etc.) are considered and the existence-uniqueness of the classical time-dependent solution is obtained. Furthermore, an asymptotic expansion (under the maximum norm) of the time-dependent solution is given and the asymptotic behavior is studied.

ISSN:0041-1450    

DOI:10.1080/00411459608204832

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459608204827

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor