Master Thesis defense by Frederik Thielsen Rohmann

Titel: Implementation and Analysis of Variance Reduction Methods in Monte Carlo Simulations 

Abstract: 

In the field of particle physics, neutron transport simulations are standard tools used for modelling and testing different environments which could prove expensive and difficult to create in real life. However, due to the stochastic nature of these simulations, these simulations can become computationally expensive, when high-accuracy results are required.

For this purpose, Variance Reduction (VR) techniques are used, which are incredibly powerful techniques, designed to enhance the accuracy of simulations at low computational cost. This thesis explains, tests and compares several of these techniques to determine their unique benefits and disadvantages, independently and in combination with each-other.

Among the Variance Techniques tested in this thesis were Source Biasing, Mesh-manipulation, LVR and the Global Variance Reduction (GVR) method. We conducted a benchmark simulation, consisting of 3 experiments designed to mimic distinct areas of a real-world nuclear assembly, and proceeded to systematically test each of the aforementioned VR techniques in comparison to the benchmark.

OpenMC was chosen as the neutron transport code, due to its’ open source nature, which allowed for the implementation of the Local Variance Reduction (LVR) technique. We implemented the LVR technique into OpenMC, and of the limited amount of parameters used for the testing of it, we found a significant increase in the computational efficiency, although at the cost of statistical accuracy. Source biasing showed the largest increase in statistical accuracy and efficiency of the methods tested, yet we argued that this method is not suitable for centralised sources. Mesh-manipulation produced slight increases to the computational efficiency at no cost to the accuracy of the simulation, but when used in conjunction with the Global- or Local Variance Reduction techniques, was found to decrease the efficiency of the latter methods. Of all the VR techniques tested, we found the Global Variance Reduction technique to be the most beneficial and robust technique in the majority of cases.

This comparative analysis is able to guide the reader into a better understanding of when to use, or not to use, the analysed methods in different neutron transport scenarios.