Asymptotically consistent reflection boundary conditions for diffusion theory

G. C. Pomraning; B. D. Ganapol

doi:10.1016/0306-4549(94)00097-X

Asymptotically consistent reflection boundary conditions for diffusion theory

G. C. Pomraning, B. D. Ganapol

Research output: Contribution to journal › Article

12 Scopus citations

Abstract

It is well known that the classic diffusion equation is an asymptotic limit of the one-speed linear transport equation. In this paper, we carry out the analysis required to obtain an asymptotically consistent boundary condition for this diffusion equation in the case of partial surface reflection. The specification of this boundary condition requires the transport theory solution to a purely scattering halfspace problem. A variational treatment is used to obtain explicit results for this halfspace problem in the general case. In the special case of purely diffuse reflection, simple considerations give exact halfspace results, and a more involved exact halfspace analysis is presented in the case of specular reflection. These exact results are used to assess the accuracy of the variational treatment.

Original language	English (US)
Pages (from-to)	787-817
Number of pages	31
Journal	Annals of Nuclear Energy
Volume	22
Issue number	12
DOIs	https://doi.org/10.1016/0306-4549(94)00097-X
State	Published - Dec 1995
Externally published	Yes

ASJC Scopus subject areas

Nuclear Energy and Engineering

Access to Document

10.1016/0306-4549(94)00097-X

Fingerprint Dive into the research topics of 'Asymptotically consistent reflection boundary conditions for diffusion theory'. Together they form a unique fingerprint.

Cite this

Pomraning, G. C., & Ganapol, B. D. (1995). Asymptotically consistent reflection boundary conditions for diffusion theory. Annals of Nuclear Energy, 22(12), 787-817. https://doi.org/10.1016/0306-4549(94)00097-X

@article{1891243509394d5493ea6ab4a84ecfae,

title = "Asymptotically consistent reflection boundary conditions for diffusion theory",

abstract = "It is well known that the classic diffusion equation is an asymptotic limit of the one-speed linear transport equation. In this paper, we carry out the analysis required to obtain an asymptotically consistent boundary condition for this diffusion equation in the case of partial surface reflection. The specification of this boundary condition requires the transport theory solution to a purely scattering halfspace problem. A variational treatment is used to obtain explicit results for this halfspace problem in the general case. In the special case of purely diffuse reflection, simple considerations give exact halfspace results, and a more involved exact halfspace analysis is presented in the case of specular reflection. These exact results are used to assess the accuracy of the variational treatment.",

author = "Pomraning, {G. C.} and Ganapol, {B. D.}",

year = "1995",

month = dec,

doi = "10.1016/0306-4549(94)00097-X",

language = "English (US)",

volume = "22",

pages = "787--817",

journal = "Annals of Nuclear Energy",

issn = "0306-4549",

publisher = "Elsevier Limited",

number = "12",

}

TY - JOUR

T1 - Asymptotically consistent reflection boundary conditions for diffusion theory

AU - Pomraning, G. C.

AU - Ganapol, B. D.

PY - 1995/12

Y1 - 1995/12

N2 - It is well known that the classic diffusion equation is an asymptotic limit of the one-speed linear transport equation. In this paper, we carry out the analysis required to obtain an asymptotically consistent boundary condition for this diffusion equation in the case of partial surface reflection. The specification of this boundary condition requires the transport theory solution to a purely scattering halfspace problem. A variational treatment is used to obtain explicit results for this halfspace problem in the general case. In the special case of purely diffuse reflection, simple considerations give exact halfspace results, and a more involved exact halfspace analysis is presented in the case of specular reflection. These exact results are used to assess the accuracy of the variational treatment.

AB - It is well known that the classic diffusion equation is an asymptotic limit of the one-speed linear transport equation. In this paper, we carry out the analysis required to obtain an asymptotically consistent boundary condition for this diffusion equation in the case of partial surface reflection. The specification of this boundary condition requires the transport theory solution to a purely scattering halfspace problem. A variational treatment is used to obtain explicit results for this halfspace problem in the general case. In the special case of purely diffuse reflection, simple considerations give exact halfspace results, and a more involved exact halfspace analysis is presented in the case of specular reflection. These exact results are used to assess the accuracy of the variational treatment.

UR - http://www.scopus.com/inward/record.url?scp=0042197895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042197895&partnerID=8YFLogxK

U2 - 10.1016/0306-4549(94)00097-X

DO - 10.1016/0306-4549(94)00097-X

M3 - Article

AN - SCOPUS:0042197895

VL - 22

SP - 787

EP - 817

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

SN - 0306-4549

IS - 12

ER -