Investigation into acceleration schemes for nuclear fuel performance mechanics solvers

Since the 1970s, nuclear safety assessments have relied on the development of numerical models to evaluate reactor performance under diverse conditions. Among these models, fuel performance codes are developed to model, predict, and assess the behaviour of nuclear fuel during operation and storage. Over recent decades, there has been a significant shift towards developing "best-estimate" codes, which aim to deliver highly accurate solutions and uncertainty quantifications, albeit at the cost of substantial computational resources and time.

OFFBEAT is a multi-dimensional fuel performance code that utilizes the OpenFOAM library for its finite volumes framework. The code often exhibits slow convergence, namely due to the complexity of multi-dimensional modelling and the inherent limitations of the Finite Volume Method (FVM). This Master Thesis investigates numerical methods to accelerate the convergence of OFFBEAT, particularly for problems that converge slowly. The segregated algorithm used to solve for the displacement field was identified as a bottleneck, especially when dealing with geometries where dimensions are significantly uneven, such as in a nuclear fuel pin. Thus, the study focuses on improving the convergence of this algorithm by exploring both physics-based and mathematics-based approaches.

A Python finite volume solver was implemented to gain practical experience in finite volume solver development and to create a lightweight, easily tuneable code for benchmarking the acceleration techniques. The methods were evaluated based on performance, complexity of implementation, and robustness, and the benchmarks showed a clear advantage in using the Newton-Krylov algorithm. By comparing different variants of the Newton-Krylov method, a mixed approach was proposed that combines the segregated algorithm with the Newton-Krylov algorithm through the residual. The implementation of this approach in the Python code proved successful and demonstrated a significant reduction in computational time.