This study presents a rigorous numerical investigation into the interplay between magnetic fields and high-speed flow dynamics across supersonic and hypersonic flow regimes. Employing advanced computational techniques, we quantify the impact of varying Mach (M) and Reynolds (Re) numbers on flow discontinuities, with particular focus on shock wave behavior under magnetohydrodynamics (MHD) conditions. The key solutions are derived for critical physical parameters such as compression rate (κ), Mach number ratio (M2M1), Cowling number ratio (C2C1), Reynolds number ratio (Re2Re1), pressure ratio (p2p1), magnetic pressure ratio (h2h1), and entropy production (S2−S1) across the shock wave. This study analyzes the combined effects of magnetic fields and viscous dissipation on shock waves in supersonic and hypersonic ideal MHD flows. A 1D model, solved using Rankine–Hugoniot conditions, reveals that stronger magnetic fields reduce post-shock pressure ratios by up to 20% while increasing downstream Mach numbers and generation. Notably, viscous, inviscid, and ideal gas flow simulations, both with and without magnetic coupling, exhibit strong alignment with the benchmark studies of Cavus “On the effects of viscosity on the shock waves for a hydrodynamical case—Part I: Basic mechanism,” Adv. Astron. 2013, 1 (2013), corroborating the numerical fidelity of our approach. This work validates its novel approach through rigorous statistical comparison with established studies, employing percentage change analysis, mean value differences, standard deviation measurements, and 95% confidence intervals. The results demonstrate significantly enhanced predictive capability relative to prior methods. Furthermore, the analysis reveals a previously under-characterized phenomenon: magnetic field effects exhibit pronounced Mach number dependence, becoming substantially more influential in hypersonic regimes compared to supersonic conditions. This finding addresses a critical gap in existing shock wave literature. This consistency underscores the robustness of our methodology in capturing MHD flow interactions under extreme velocity conditions.
Dunna et al. (Mon,) studied this question.