A cell-based population control of Monte Carlo particles for the global variance reduction for transport equations

TL;DR

This paper introduces a novel cell-based population control method for Monte Carlo particles to improve variance reduction in transport equation simulations, with theoretical analysis and numerical validation against benchmarks.

Contribution

It presents a new population control algorithm based on cell-based methods and analyzes two types of splitting, advancing variance reduction techniques in Monte Carlo transport simulations.

Findings

The new algorithm improves variance reduction efficiency.

Theoretical analysis compares energy-conservative and non-conservative splitting.

Numerical tests demonstrate effectiveness against benchmark problems.

Abstract

We present a population control method with sampling and regulation steps for Monte Carlo particles involved in the numerical simulation of a transport equation. We recall in the first section the difficulties related to the variance reduction methods in the general framework of transport equations; we continue with a brief presentation of the mathematical tools invoked when solving the radiative transport equations and we focus on the importance of the emission and control of existing Monte Carlo particles. The next part discusses several novel methods based on the cell-based population control method proposed earlier. To this end, we analyze theoretically two types of splitting: one is conservative in energy (at the particle level) and the other is not. Thanks to these results, a new algorithm is introduced that uses the cell-based population control method and a spatial distribution. A numerical comparison of the different types of splitting is proposed in a simplified framework, then the various algorithms presented are compared against two benchmarks : the propagation of a Marshak wave and the propagation of two waves having different intensity and speed scales. To carry out these last tests, we use the multi-physics code FCI2.