Uniform variance method for accelerated Monte Carlo criticality calculation

Highlights: • The Monte Carlo method has advantages in simplicity and flexibility, so the authors always pay attention to the simplicity and flexibility when developing some new Monte Carlo algorithms. The development process of UVM method had fully considered the fundamental framework of the Monte Carlo criticality calculation and the special computing characteristic of the Monte Carlo method. • The UVM method provides a fast and convenient method to calculate the weight windows parameters and the source bias parameters, so it can be used effectively for variance reduction. The new ideas of the UVM method are:• Originality: calculate and update the weight windows parameters and source bias parameters during the inactive cycles, which has never been done before. • Simplicity: the implementation of the UVM method is relatively simple, the logic of the algorithm is clear, and it can be understood easily. • Effectiveness: based on the test on a modified C5G7 model, the AV.FOM is improved by at least 26 times with different neutron population per cycle and different number of cycles, and the AV.FOM is improved by at least 37 times with different initial fission sources. The problem of the non-uniform distribution of relative errors is encountered during the Monte Carlo criticality calculation, which not only reduces the efficiency and the accuracy of some local tallies, but also affects the stability of the Monte Carlo multi-physics coupling calculation. To solve this problem, the uniform variance method is proposed. In this method, the global information is recorded and updated during the inactive cycles, and the source bias technique and the weight windows technique are combined to achieve the uniform distribution of relative errors. The modified C5G7 benchmark is tested by the uniform variance method, and it is found that the variance is reduced in almost all tallies compared with that of the direct simulation. So the uniform variance method is helpful for the global variance reduction, and can be used for the acceleration of the Monte Carlo criticality calculation.