A numerical method for solving the two-dimensional neutron diffusion equation

✍ Scribed by R.M. Pearce

• Publisher: Elsevier Science
• Year: 1956
• Weight: 725 KB
• Volume: 2
• Category: Article
• ISSN: 0891-3919
• DOI: 10.1016/0891-3919(55)90044-9

✦ Synopsis

Conventional numerical methods for solving differential equations on a two-dimensional mesh are adapted to solving the one-group pile equation. The method yields the neutron density and the radial Laplacian in a standard manner which is not dependent on the number of control rods or other lattice irregularities.

The procedures for calculation with a desk machine and with a large digital computer differ in certain respects, and are discussed. As an example, the distribution of neutron density is given for a reactor with seven asymmetrically inserted control rods.

?? This is a further advantage of using a hexagonal mesh. A square mesh is most commonly used in relaxation problems, and the corresponding difference operator in this case is correct only in the thirdorder terms.