A Finite Volume and Levenberg–Marquardt Optimization Framework for Benchmarking MHD Flows over Backward-Facing Steps

Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement, and biomedical applications. This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward-facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an angle. The novelty of this work lies in employing an in-house finite-volume solver with a collocated grid configuration that directly applies a Newton–like method, in contrast to conventional iterative approaches. The computed hydrodynamic results are validated with experimental and numerical studies for an expansion ratio of two, while the MHD case is validated for Reynolds number R e = 380 and Stuart number N = 0.1 . One of the most important findings is the reduction in the reattachment point and simultaneous increase in pressure as the magnetic field strength is amplified. The magnetic field angle with the greatest influence is observed at φ = π / 2 , where the main recirculation vortex is substantially suppressed. These results not only clarify the role of magnetic field orientation in BFS flows but also lay the foundation for future investigations of three-dimensional configurations and coupled MHD–thermal applications.