TOWARDS A NEW ERA OF NUMERICAL SIMULATIONS: 4TH-ORDER ACCURATE NUMERICAL MODELING OF RELATIVISTIC MAGNETIC RECONNECTION

Relativistic magnetic reconnection is a well-established, efficient, and universal mechanism for particle acceleration and burst-like emissions observed in phenomena such as solar flares, pulsar and black hole magnetospheres, fast radio bursts, and the coronae of accretion disks powering relativistic jets in AGNs and microquasars. Among the various reconnection scenarios, the ideal tearing mode instability has resolved two major issues in the macroscopic resistive MHD framework: the paradox of super-tearing instability in Sweet-Parker current sheets and the need for a mechanism to explain fast, spontaneous magnetic reconnection. Despite its significance, current three-dimensional models struggle to capture the ideal tearing mode instability on dynamical timescales due to computational limitations. Loworder numerical methods and traditional CPU-based architectures are insufficient to handle the high grid resolutions required to model the small dissipation length scales associated with low resistivity. This thesis presents the complete implementation of a genuinely 4th-order accurate finite volume method for solving the classical and special relativistic MHD equations in both ideal and resistive regimes. The novel scheme introduces key advancements, including pointwise-to-pointwise reconstructions, the use of generic upwind constrained transport averaging, and sophisticated limiting strategies featuring a discontinuity detector and order reduction procedures. A standout feature of the resistive special relativistic method is its implicit-explicit approach, making it one of the first 4th-order accurate finite volume schemes for multidimensional partial differential equations with stiff terms. The method, which will be publicly available in the first major GPU code release (gPLUTO), significantly reduces computational demands, halving the grid resolution required by traditional paradigms and enabling the exploration of dissipation regimes that remain widely unexplored. The scheme is also among the first 4th-order accurate finite volume methods optimized for modern GPU-based computational infrastructures. Its capabilities are demonstrated through the first set of 4th-order accurate, GPU-accelerated, three-dimensional simulations of ideal tearing dynamics within the resistive special relativistic MHD framework. The proposed simulations show a rapid conversion of magnetic energy into heat, with very few regions where the electric field becomes strong enough to promote particles’ acceleration. Compared to the 2D counterparts where a saturation phase is eventually reached, 3D simulations see the onset of secondary reconnecting instabilities along with turbulence, which concur in the final disruption of the tearing current sheet and of the flux rope. Turbulence plays a key role also in forming additional current sheets and potentially triggering secondary reconnection events, further releasing magnetic energy.