An error estimate for the multigroup method with application to shielding calculations

A variable energy version of the rod model is described for a transport situation in which the multigroup method is of interest, with application to shielding calculations. The multigroup approximation is formulated in detail and the appropriate convergence criteria is given considerations concerning the reference spectrum used in defining the multigroup approximation are briefly discussed. The convergence theorem for the multigroup method is based on a discrete version of the Lax Equivalence Theorem, and the resulted is formulated. The proof of the convergence theorem for the multigroup method is stated and outlined. The stability and consistency results necessary to apply the Lax Equivalence Theorem are established. A detailed proof of the convergence theorem is also given and its hypotheses discussed further. It is shown that the associated error estimate suggests the maximum possible error in a given multigroup approximation is proportional to the maximum fluctuations of the total cross section over all energy groups and an example is shown to test this conclusion. (U.K.)