Why are the P(n) and S(n) Methods Equivalent.

Cullen, D. E.

Technical Information Center Oak Ridge Tennessee

关键词: Spherical harmonics;    Boltzmann equations;    Discrete ordinate method;    Polynomials;    Physics;   

RP-ID  :  DE200415006206

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

The author assumes that the reader is familiar with the Spherical harmonics, Pn, method and the discrete ordinates, S(sub n), method; for a derivation of the equations used in these methods. I will only discuss the Boltzmann equation in one dimension, and the Sn method using Gaussian quadrature. I will do this merely to simplify the following discussion; once you understand the concepts presented here you can easily extend the conclusions to more general situations. Why are the spherical harmonics P(sub n) and discrete ordinate S(sub n) methods, or more correctly the P(sub n) and S(sub n+1) methods, equivalent, e.g., P(sub 3) is equivalent to S(sub 4). When the S(sub n) method uses a Gaussian quadrature most textbooks will tell you that both methods are equivalent to assuming that the angular flux can be represented by a Legendre polynomial expansion of order n.