Abstract

In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SP_N) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SP_N equations are needed. Nonclassical SP_N equations to model isotropic scattering have been derived, and the nonclassical SP₁ equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SP_N equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP₁ equation with anisotropic scattering.

摘要

在非经典输运中，将自由路径长度变量s建模为自变量，并推导了包含s的非经典线性玻尔兹曼输运方程。为了对扩散状态下的输运进行建模，已经成功地使用了简化的球谐方程（SP _N）。为了模拟扩散状态下的非经典输运，需要SP _N方程的非经典形式。推导了模拟各向同性散射的非经典SP _N方程，并且非经典SP ₁已经确定了具有各向异性散射的方程，但是用于导出方程的方法不能导出高阶方程。本文提出了一种新方法，该方法将能够导出具有各向异性散射的所有非经典SP _N方程。提出了此方法，并将其用于生成这些方程式中的第一个，并且该方法等效于先前推导的具有各向异性散射的非经典SP ₁方程。