Next Generation Algorithms for Magnetically Confined Fusion Reactor Simulations

Abstract

This work develops and implements advanced computational algorithms for whole-system nuclear fusion reactor simulations, with a focus on predicting and understanding non-linear MHD (magnetohydrodynamics) plasma instabilities and disruption events. The objective is to model all reactor regions (plasma, quasi-vacuum, and containment vessel) within a single three-dimensional simulation on a Cartesian reference frame, diverging from traditional physics-driven mesh alignment methods. Key challenges include handling disparate length and time scales, highly non-linear plasma dynamics, anisotropic behaviour, discretising complex boundaries and material interfaces, preserving non-grid-aligned equilibria, ensuring high-order accuracy, capturing shocks, and maintaining the divergence-free condition of the magnetic field. Adaptive multi-grid solvers are used to compute steady-state plasma equilibria, while sharp-interface finite volume methods resolve transient visco-resistive MHD flows. High-order Godunov-type shock-capturing schemes and adaptive mesh refinement enhance accuracy and efficiency for disparate scales and anisotropy, while ghost fluid methods facilitate the discretisation of complex embedded boundaries. Magnetic divergence errors are controlled through constrained transport and divergence-cleaning, and well-balancing techniques are explored for the preservation of non-trivial non-grid-aligned equilibria. By integrating these components into a unified Cartesian framework, this work enables MHD simulations in complex geometries with realistic initial data and scalable parallel performance, marking a significant advancement in tokamak fusion plasma modelling. Additionally, an original semi-implicit numerical scheme is developed to treat the Alfvén and fast waves of MHD implicitly, effectively removing the overly restrictive stability constraint imposed by the CFL (Courant-Friedrichs-Lewy) condition in MHD simulations. Although this scheme is not yet combined with the rest of the framework, it represents a significant step toward improving the stability and efficiency of MHD simulations with the framework in future work. The framework is validated against numerous MHD benchmark problems, both compressible and incompressible, including various equilibrium configurations and visco-resistive test cases. Realistic case-studies, including edge localised modes (ELMs) and violent disruption events, highlight its effectiveness in simulating tokamak instabilities, providing accurate and computationally efficient solutions alongside robust shock-capturing capabilities.