Over de ontwikkeling van een hoge-orde Flux Reconstructie-oplosser voor zonneplasma’s en ruimteweertoepassingen

At the heart of our solar system lies a restless star, ceaselessly hurling charged particles and magnetic fields into space and shaping a turbulent environment with variable conditions, which is known as space weather. While this background activity is ever-present, it is the violent outbursts, coronal mass ejections (CMEs), that pose the greatest threat: capable of disrupting satellite operations, communications, and power grids, and exposing astronauts and passengers on polar flights to dangerous levels of radiation. These risks make accurate space weather forecasting both a scientific challenge and a societal necessity. Numerical prediction of these phenomena relies on large-scale magnetohydrodynamic (MHD) simulations that must resolve complex, multi- scale plasma structures. Current state-of-the-art operational models are built on finite-volume (FV) methods that, being limited to at most second-order spatial accuracy, require grids with millions of elements to achieve sufficient fidelity, resulting in high computational costs and limited forecasting speed. This thesis introduces and validates a fundamentally different approach: the use of high-order Flux Reconstruction (FR) methods for heliospheric MHD simulations. High-order schemes offer significantly higher spatial accuracy than traditional FV solvers, enabling accurate results on much coarser grids and paving the way for faster and more efficient forecasts. The FR framework is implemented within the modular COOLFluiD platform, which is extended from tensor-product to simplex elements to allow for flexible unstructured grids, and enhanced with robust shock-capturing techniques and dedicated high-order data handling libraries. The solver supports a wide range of governing equations, from compressible Euler and Navier-Stokes to ideal and resistive MHD, allowing for polynomial orders up to P = 9. Systematic verification and validation demonstrate the method's versatility across diverse flow regimes, from subsonic and supersonic test cases to realistic space plasma applications. Most notably, the FR solver is applied for the first time to inner-heliospheric simulations of the solar wind, including steady-state, time-evolving, and CME-driven scenarios. Direct comparisons with EUHFORIA, a widely used operational model, show that FR reproduces large-scale solar wind structures and one-dimensional profiles with remarkable fidelity while using grids with up to ∼100× fewer elements. In realistic solar wind cases, FR achieves comparable accuracy with over 6× fewer degrees of freedom and substantially reduced computational runtime, 2.4× to 2.8× faster per degree of freedom than EUHFORIA, confirming that the theoretical advantages of high-order methods translate into tangible efficiency gains for realistic space weather applications. These results establish a versatile high-order CFD framework that successfully bridges accuracy and efficiency for large-scale heliospheric modelling. By enabling accurate predictions on drastically coarser grids, high-order FR methods represent a transformative step toward operational space weather forecasting, capable of delivering faster and more reliable results as upstream coronal models and computational resources continue to advance.