THE ANALYTICAL SOLUTION TO THE 1D MULTIGROUP DIFFUSION EQUATION IN HETEROGENEOUS MEDIA
讲座名称：
THE ANALYTICAL SOLUTION TO THE 1D MULTIGROUP DIFFUSION EQUATION IN HETEROGENEOUS MEDIA
讲座时间：
2015-05-26
讲座人：
BARRY D. GANAPOL
形式：
校区：
兴庆校区
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讲座内容：
题目: THE ANALYTICAL SOLUTION TO THE 1D MULTIGROUP DIFFUSION EQUATION IN HETEROGENEOUS MEDIA
报告人:PROF. BARRY D. GANAPOL
UNIV. ARIZONA, USA
时间:5.26(星期二)上午10:10
地点:主楼D-106
THE ANALYTICAL SOLUTION
TO THE
1D MULTIGROUP DIFFUSION EQUATION
IN HETEROGENEOUS MEDIA
B. D. Ganapol
Department of Aerospace and Mechanical Engineering
University of Arizona, Tucson AZ, USA
Ganapol@cowboy.ame.arizona.edu
ABSTRACT
The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane, cylindrical and spherical media will be presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup equation as a series of one-group equations. Customized eigenmode solutions to the one-group diffusion operator then represent the homogeneous modal solutions in a single homogeneous region. Once the homogeneous solution is known, the particular solution naturally emerges from variation of parameters. The resulting analytical expression is numerically implemented through recurrence or analytically through an additional analytical solution of the recurrence relation. We end with a benchmarking application of a finite difference scheme and implications for time dependent diffusion theory solutions.
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