摘要:

We present a new spatial discretization method, which enforces conservation on quadrilateral subcells in an arbitrarily connected grid of polygonal cells, for two-dimensional radiative transfer problems. We review what is known about the performance of existing methods for optically thick, diffusive regions of radiative transfer problems, focusing in particular on bilinear discontinuous (BLD) finite-element methods and the simple corner-balance (SCB) method. We discuss the close relation of the SCB and BLD methods, and how they differ. By careful analysis, we relate specific properties of the SCB solution to specific approximations in the SCB method. We then build our new method by discarding those SCB approximations that lead to undesirable properties and carefully constructing new approximations designed to yield more desirable properties. We compare BLD, SCB. and the new scheme on a series of test problems in slab and XY geometries; numerical results invariably agree with predictions of the analysis. The new method matches SCB in thick diffusive regions, as it was designed to, but vastly outperforms SCB given cells of fine and intermediate optical thickness, where it achieves results comparable to BLD.

ISSN:0041-1450    

DOI:10.1080/00411459708017924

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Starting from the transport equation, a systematic homogenization theory and a self-consistent de-homogenization theory for fuel assemblies have been developed using a multiple-scales asymptotic expansion method. The resulting theory provides a framework for coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is carried out through second order in a small parameter—the ratio of the neutron mean free path to the reactor characteristic dimension. Introducing two spatial scales—a fast scale for the rapid variation of the flux over a fuel assembly and a slow scale for the slow variation of the flux over the whole core—into the neutron transport equation for a three-dimensional heterogeneous medium, the development systematically yields: an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections, and assembly-surface flux discontinuity factors. The analysis shows that the solution of the assembly-homogenized global diffusion equation leads to a reactor eigenvalue 1/keffthat is second order in the small parameter, and a heterogeneous transport theory angular flux that is leading order. The reaulting framework also provides a natural and self-consistent procedure for the reconstruction of the local heterogeneous angular fluxes which makes it possible to calculate the pin ower.

ISSN:0041-1450    

DOI:10.1080/00411459708017925

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The fission chain paradigm is used to analyze the underlying stochastic-ity of the neutron transport equation. The analysis is limited to one-group neutrons in an infinite, homogeneous medium, and is done in the generation and in the time-dependent descriptions but includes external sources and neutron precursors. We give general results for average values and characterize the validity of the deterministic, mean-value description with the variance of the underlying stochastic process. We analyze the stochastic behavior of the one-point kinetic model and give asymptotic expressions for mean values and variances. In the absence of sources, we have also analyzed the probability of extinction of the fission chain and proved classical results. In particular, we show that a critical system with a continuous supply of target nuclei cannot maintain a self-sustained fission chain. This result is shown to be true even in the presence of precursors. We prove, however, that an idealized thermal reactor, infinite in size, can maintain a semblance of a stationary distribution for as long as a day without external intervention.

ISSN:0041-1450    

DOI:10.1080/00411459708017926

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Numerical solutions for the classical, monoenergetic albedo and Milne problems for a half-space are obtained from a numerical Laplace transform inversion and the nonlinear integrodifferential equation for the source function. Anisotropic scattering and an azimuthally-dependent incident illumination are treated.

ISSN:0041-1450    

DOI:10.1080/00411459708017927

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

One of the basic particle transport problems consists of a narrow beam of light normally incident on a planar surface. As the beam progresses deeper into the system, it decays due to absorption, and broadens or “flattens” due to scattering. Closed-form expressions for the amplitude and root-mean-square radius of the beam, as functions of depth, are reported here for both the transport and diffusion equations. Also, the transport and diffusion results are compared numerically.

ISSN:0041-1450    

DOI:10.1080/00411459708017928

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The problem of the transverse spatial spreading and angular dispersion of a pencil beam of charged particles with depth in a highly forward scattering medium, as originally posed by Fermi, is given a stochastic interpretation. It is shown that the spatial and angular relaxation of the beam is equivalently described by the random walk, or Brownian motion, of a particle in phase space. The joint probability distribution function of the particle's lateral position and associated direction is shown to satisfy a Fokker-Planck equation, which reduces to Fermi's equation for the angular flux if the particle diffusion coefficient is equated to the transport cross section. This stochastic analogy enables explicit solutions to be constructed with ease using well known results from the theory of Gaussian stochastic processes.

ISSN:0041-1450    

DOI:10.1080/00411459708017929

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

An expression is derived for the first-order change in the ratio of linear functionals of the fundamental solution of the neutron transport equation due to a perturbation in the boundary condition of the system. The perturbation formula is derived in the context of energy dependent transport theory. The multigroup formulation is also given. Two numerical examples are used to verify the correctness of the formalism. As an application, use of this method for improving spatial homogenization techniques is also discussed

ISSN:0041-1450    

DOI:10.1080/00411459708017930

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

A systematicnonperturbaiivederivation is presented of a whole hierarchy of closed systems of moment equations corresponding to any classical kinetic theory that describes a gas of identical particles under the influence of an external potential. The closure has two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit The second modifies the collision operator so that members of the hierarchy beyond the second also recover the correct Navier-Stokes behavior. This is achieved through a generalization of the BGK collision operator.

ISSN:0041-1450    

DOI:10.1080/00411459708017931

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The two-region Milne problem results of Ganapol and Pomraning are used in a proposed solution to an inverse transport problem in which there are two adjacent, optically-thick, isotropic-scattering layers. Equations are obtained for approximately estimating the mean number of secondaries of each region using only the normally-directed angular fluxes and the scalar fluxes and currents at the external boundaries. The impracticality of extending the analysis to two regions with anisotropic scattering or to more than two isotropic-scattering regions is discussed, as well as limitations of the proposed solutions.

ISSN:0041-1450    

DOI:10.1080/00411459708017932

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The transport of radiation through a random array of purely absorbing slabs is considered assuming that the cross section of the slabs fluctuates according to binomial statistics. An exact solution is constructed for the transmission factor through N slabs and the mean value and variance calculated. It is also shown how the complete probability distribution may be recovered. The results are extended to the case of two different types of slab material and thickness and also to the case where the slab thickness is random subject to a constant total thickness of the system. Simple results are obtained and these are compared with the solution of an analogous problem using the dichotomic Markov process method favored by Pomraning and his co-workers. No particular conclusions are drawn regarding the relative merits of these two statistics and the matter is left open for futher discussion.

ISSN:0041-1450    

DOI:10.1080/00411459708017933

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor