Hybrid solvers for reactor modelling: matrix-based and matrix-free approaches on voxel-dominated meshes

Abstract

Simulating neutronics and thermal hydraulics within nuclear reactor cores is computationally intensive, not only because of the complexity of the governing equations but also because of the intricate geometries involved. Solving the Boltzmann transport and Navier-Stokes equations for a full core representation typically relies on unstructured meshes, which, while highly flexible, can substantially increase computational costs regarding memory and solving time. Cartesian meshes with Finite Elements (FE) offer a faster alternative, potentially improving computational speed by an order of magnitude due to direct memory addressing. However, they necessitate finer grids to accurately capture the boundary details of non-Cartesian surfaces, which can offset these gains by increasing solver times. To address this challenge, a new meshing algorithm is proposed in conjunction with hybrid, matrix-based and matrix free, solver technologies. It employs a geometry-conforming boundary method using voxel-dominated Cartesian meshes. This method enables accurate boundary representation at arbitrary resolutions, which can be adjusted to resolve the physics to the desired level of accuracy rather than strictly to capture geometric detail. This is combined with a hybrid solver for fluid flows to different regions of a problem in order to increase efficiency when resolving the boundary. This article demonstrates the method’s application to Computational Fluids Dynamics (CFD) and neutronics problems relevant to reactor physics, showcasing its accuracy, convergence, numerical stability, and suitability for handling complex geometries.