A Multilevel Approach for Direct Core Calculation Schemes

Abstract

A method of dynamic homogenization was recently proposed as an alternative technique for three-dimensional (3D) core calculations using a direct approach. This technique allows for producing homogenization parameters for a subdomain within the core at its actual state, and offers the advantage of avoiding off-line calculations, cross-section interpolations, and expensive 3D transport calculations. The methodology has shown a remarkable reduction in computational cost compared to 3D transport. However, the application of direct calculation schemes in multiphysics and multicycle problems still demands an extensive use of computational resources. Within the framework of traditional two-step calculations, several multilevel schemes have been developed to accelerate lattice calculations for the generation of the multiparameter cross-section libraries. With a similar objective, this work investigates how the multilevel approach can be applied within the framework of direct calculation schemes and discusses how depletion calculations may be performed. The objective is to enhance their performance and reduce memory requirements in favor of a high-fidelity model of the matter behavior in the reactor. We have then identified suitable flux solvers for each level and explored various homogenization options. We tested the methodology in a 3D pressurized water reactor core problem inspired by the TVA Watts Bar Unit 1 Multi-Physics Multi-Cycle OECD/NEA Benchmark, and performed a comparative analysis to assess the accuracy and computational efficiency of these new calculation schemes against direct single-level calculations and a two-step calculation based on pin-by-pin homogenization, as well as Monte Carlo simulations. Our analysis proves that the computational resources required to solve the full-core problem using a multilevel scheme are significantly reduced, and the best computational features are provided by multilevel dynamic homogenization. Furthermore, we observed that the multilevel approach not only allows for speedup, but can also be advantageously applied in order to improve the accuracy of the final solution of a calculation scheme when the core solver relies on an approximate transport operator.