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

Spyridon Katsoudas, Grigorios Chrimatopoulos, Michalis Xenos and Efstratios Tzirtzilakis ()
Additional contact information
Spyridon Katsoudas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Grigorios Chrimatopoulos: Department of Mechanical Engineering, University of the Peloponnese, 1 M. Aleksandrou Str, Koukouli, 263 34 Patras, Greece
Michalis Xenos: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Efstratios Tzirtzilakis: Department of Civil Engineering, University of the Peloponnese, 1 M. Aleksandrou Str, Koukouli, 263 34 Patras, Greece

Mathematics, 2025, vol. 13, issue 18, 1-18

Abstract: 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.

Keywords: backward-facing step; magnetohydrodynamics; finite volumes method; direct numerical solution; point of flow reattachment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/2953/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/2953/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:18:p:2953-:d:1748036

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().