Mathematical and computational modelling of magnetohydrodynamics

Abstract

Astrophysical systems present significant challenges due to the vast range of phenomena and scales they encompass. Magnetohydrodynamic (MHD) models are particularly integral to the study of such systems, with applications spanning Stellar Astrophysics, such as solar wind and magnetoconvection, to Extragalactic Astrophysics, including modeling the interstellar medium. Numerical simulations play a crucial role in advancing our understanding of these complex systems by providing approximate predictions of their behavior under predefined conditions. However, the computational demands of MHD equations make it essential to achieve these simulations within realistic timeframes. To address this, most advanced MHD simulation codes are written in low-level programming languages, such as C, C++, and FORTRAN. While powerful, these languages are challenging to interpret, which steepens the learning curves for new users. Furthermore, existing simulation codes often require separate software for data visualization and analysis, adding complexity and delaying insights. This dissertation presents a Python-based code for astrophysical MHD simulations that addresses these limitations by offering an accessible and user-friendly alternative. The code integrates tools for real-time visualization and analysis, enabling users to monitor the evolution of their simulations as they run. To minimize wasted computational resources and user effort, the code includes automatic error-checking mechanisms to identify input parameters and initial conditions that could lead to numerical instabilities. The performance and accuracy of the code are validated through standard test problems, including the Brio-Wu shock tube, the Orszag-Tang vortex, and a MHD spherical blast wave. Detailed descriptions of the algorithms and methodologies implemented are provided, highlighting the potential of this tool to streamline MHD research.