Analysis of normal shock propagation in Van der Waals gas under turbulent flow with magnetic field by Levenberg–Marquardt algorithm

This study investigates the propagation of normal shock waves in Van der Waals gas subjected to turbulent flow and exposed to a vertical magnetic field, providing insights into the complex shock dynamics of non-ideal gases. The findings have significant applications in fields such as aerospace engineering, plasma physics, meteorology, and industrial processes. The objective is to analytically assess shock wave behavior, focusing on how turbulence intensity, magnetic field strength, and gas molecule volume affect shock strength. Modified Rankine–Hugoniot boundary conditions are used to analyze shock wave propagation, incorporating the key variables. The relationship between velocity and turbulence strength in adiabatic turbulent gas flow is also examined, with Levenberg–Marquardt algorithm-validated backpropagated neural networks employed to model the complex interactions under non-adiabatic conditions. The results show that higher magnetic fields increase shock strength by raising the Mach number for a given density ratio, while turbulence enhances pressure as shock waves propagate, significantly influencing shock dynamics. The study emphasizes the critical role of magnetic fields in shock wave behavior within turbulent, non-ideal gas flows.