A Hybrid Monte Carlo-Deterministic Method for Global, Time-Dependent Transport Calculations

Allan Wollaber, University of Michigan

Photo of Allan Wollaber

A new hybrid Monte Carlo-Deterministic technique is presented for simulating global transport problems – problems in which flux estimates are desired at all physical locations in the system. This technique has two steps: first, an inexpensive deterministic global estimate of the forward flux is obtained; then Monte Carlo is used to estimate the multiplicative correction to the deterministic flux estimate. We call the multiplicative correction to the deterministic flux the correcton flux, and the Monte Carlo particles that estimate this flux correctons. For deep-penetration problems, the correcton flux has significantly less spatial variation than the physical flux. Therefore, the Monte Carlo process automatically distributes correctons much more uniformly across the system than it distributes Monte Carlo particles for the original angular flux. In the “deep” parts of the problem, near the edge of a wavefront, this results in a greatly-reduced variance and a greatly-increased figure of merit.

Abstract Author(s): Allan Wollaber, Edward Larsen