Equivalent source estimation for use in solving the fixed source boltzmann transport equation by Monte Carlo methods

Two surface equivalent source estimators were developed for Monte Carlo solution of the fixed source Boltzmann transport equation. These estimators are analogous to the contributon Monte Carlo estimator, i.e., volume equivalent source estimator. The surface estimation schemes were calculationally demonstrated to provide superior precision and benefit over contributon Monte Carlo for full transport calculations. They were also demonstrated to be applicable to void streaming calculations in which transport in the surrounding medium was replaced with albedo surfaces. Using a surface equivalent source estimator, the variance reduction mechanisms of contributon Monte Carlo and surface equivalent source estimation were investigated and shown to be equivalent to those of the standard biasing scheme, splitting.

The combination of simultaneously calculated standard and equivalent source estimates of the response was formally investigated. It was shown that the conditions for optimized combination of these estimates are restricted such that combinations in most cases would not result in a significant gain in benefit.

Guidelines, primarily for use of the vacuum surface equivalent source estimator, were formulated based on the understanding of the variance reduction mechanisms developed in this research, calculational experience obtained in this work, and previously reported experience with contributon Monte Carlo and surface splitting. The guidelines are not, in general, expected to provide optimum results but will provide the insight and guidance to allow significant gains in benefit from use of the procedure in either full transport or void streaming problems.