Legendre expansion in multilayer slab geometry

The monoenergetic integral transport equation for a multilayer slab geometry has been solved by the Legendre expansion method. The method utilizes an expansion of the flux density in each layer in Legendre polynomials of the position co-ordinate. The use of these polynomials makes it possible to calculate most of the resulting matrix by means of recurrence formulae. These formulae have been obtained by a procedure which is an extension of Carlvik's method for homogeneous slab. A code (MULREG) has been written for this purpose. Using MULREG a series of calculations have been performed for a homogeneous slab with vacuum boundary conditions. The slab has been divided into NR number of regions and in each region flux is expanded into Legendre polynomials of order NSI. For a particular value of NR, the NSI varies from 0 to 4. The effective multiplication factor ksub(eff) of the slab is calculated. By comparing the computational time for all the cases, it is studied as how severe it is to consider the flat flux approximation (conventional collision-probability approach) as compared to a case when more terms in the flux expansion are considered per layer. (author)