A Comparative Analysis of High-resolution Shock-capturing Schemes for Two-dimensional Magnetohydrodynamic Simulation of Flux Emergence in the Solar Atmosphere

Abstract This study presents a comparative analysis of high-resolution shock-capturing schemes in two-dimensional magnetohydrodynamic (MHD) simulations of magnetic flux emergence in the solar atmosphere. We evaluate four distinct reconstruction techniques based on recent improvements to the weighted essentially nonoscillatory (WENO) and targeted essentially nonoscillatory schemes. While these schemes have proven successful for the Euler equations of gas dynamics, their effectiveness in MHD simulations remains relatively unexplored. Our implementation combines the Harten–Lax–van Leer-discontinuities approximate Riemann solver for accurate flux computations, the generalized Lagrangian multiplier method for divergence control, and a third-order strong stability preserving the Runge–Kutta scheme for time integration. Numerical experiments reveal that these advanced schemes provide significant improvements in both accuracy and robustness in capturing complex MHD phenomena such as magnetosonic waves, MHD shocks, and magnetic buoyancy-driven instabilities. Among the tested methods, IMWENO-P proves to be the most physically consistent, effectively reproducing energy redistribution and compression patterns in line with theoretical predictions. These findings offer valuable insights into the strengths and limitations of each approach for simulating magnetic flux emergence dynamics.