Flux-Stagger: A Vectorized Staggered-Mesh MHD Solver for Magnetorotational Instability in Accretion Disks

This work presents the development of Flux-Stagger, a fully vectorized Python-based 2D magnetohydrodynamic (MHD) solver designed to simulate the Magnetorotational Instability (MRI) in Keplerian accretion disks. The solver employs a staggered-mesh Constrained Transport (CT) scheme to rigorously maintain the divergence-free condition (∇·B = 0), ensuring physical consistency without artificial correction methods. The implementation leverages NumPy-based vectorization for efficient computation on standard hardware. The simulation successfully reproduces the key evolutionary phases of MRI, including the initial laminar state, exponential growth, non-linear saturation, and transition to sustained turbulence. A magnetic energy growth rate of γ ≈ 0.182 is obtained through log-linear fitting, aligning closely with theoretical predictions. These results demonstrate that high-fidelity MHD behavior can be captured using lightweight computational frameworks, providing a foundation for further extensions such as 3D simulations and advanced astrophysical modeling. GitHub Repository: https://github.com/Avinash1533/2D-MHD-MRI-Simulation