Hyperbolic PDE models for dynamo-type magnetic field behaviour

By introducing finite propagation speeds and wave-like magnetic transport effects, hyperbolic partial differential equation (PDE) models are very useful in describing the behaviour of the magnetic field of dynamo type as it passes through an electrically conducting medium.In this study, we have created a hyperbolic dynamo model using the conservation principles and magnetohydrodynamic theory to study the evolution of the magnetic field under transient conditions.This is done by using stable numerical algorithms in both space and time for the governing equations and by using an efficient computational algorithm to accurately simulate them.The proposed methodology is able to more realistically represent magnetic induction, diffusion and propagation phenomena than classical parabolic formulations.Stabilization, decrease in numerical dispersion and prediction of transient magnetic structures is proven with numerical results.The framework developed is a framework that is mathematically sound which can be used for the analysis of astrophysical, geophysical and engineering dynamo systems and can be used as a mathematical tool in future studies of more complex dynamo systems in astrophysics, geophysics and engineering.