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Next: Method Derivation Up: 1996_NECDC Previous: Introduction

Method Overview

The equation to be solved is given by \begin{displaymath}\alpha \frac{\partial \Phi}{\partial t} - \mbox{$\mbox{$\stac...
...box{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{J}$} \; ,
\end{displaymath}
which can be written

\begin{eqnarray}\html{eqn2}
\alpha \frac{\partial \Phi}{\partial t} + \mbox{$\m...
...\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{J}$} \; ,
\end{eqnarray}


where

\begin{eqnarray}\html{eqn4}
\Phi & = & \mbox{\hspace{2em} Intensity} \\
\mbox...
...ongrightarrow}}{J}$} & = & \mbox{\hspace{2em} Flux Source Term} .
\end{eqnarray}


Everything in this equation is assumed to be known, with the exception of $ \Phi$ and $ \mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{F}$}$ at the new time step. This equation has an extra term from the standard diffusion equation, the $ \mbox{$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{\nabla}$} \cdot$}$$ \mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{J}$}$ term, which allows it to model the P1 and SPN equations.

The new method shares these properties with the method described in ##more92 (##more92):

In addition, the new method handles unstructured meshes and is multi-dimensional. The geometries that can be handled by the new method are listed in Table 1.

Table 1: The geometries that can be handled by the new method, all of which have an unstructured (arbitrarily connected) format.
Dimension Geometries Type of Elements
1-D spherical, cylindrical or cartesian line segments
2-D cylindrical or cartesian quadrilaterals or triangles
3-D cartesian hexahedra or degenerate hexahedra (tetrahedra, prisms, pyramids)


next up previous
Next: Method Derivation Up: 1996_NECDC Previous: Introduction
Michael L. Hall