A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow

Ebutalib Çelik

doi:10.53570/jnt.1733901

A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow

Abstract

This study presents a new approach to solving magnetohydrodynamic (MHD) flow problems in complex geometries using a polynomial-based Radial Basis Function-Generated Finite Difference (RBF-FD) method within a non-overlapping domain decomposition framework. It partitions the domain, specifically an L-shaped cavity with a single lid-driven, into simpler subregions where classical finite difference methods are applied, and employs the method RBF-FD at the interface points. Unlike traditional RBF approaches that require mostly shape parameter optimization, this study uses a polynomial basis function to determine derivative weights. It validates the method on benchmark lid-driven cavity problems and extends it to analyze MHD flows under various magnetic field strengths $M\in\{10,50,100\}$ and orientations $\alpha\in\{0^\circ,45^\circ,90^\circ,135^\circ,180^\circ\}$. The computational results illustrate the influence of magnetic field angle and cavity aspect ratio $\left(h_1,h_2\right)$ on vortex formation, revealing complex bifurcation behaviors unique to L-shaped geometries.

Keywords

Supporting Institution

Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University

Project Number

FHD-2024-4633

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: FHD-2024-4633.

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Details

Primary Language

English

Subjects

Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Ebutalib Çelik ^*
0000-0002-4500-4465
Türkiye

Early Pub Date

September 30, 2025

Publication Date

September 30, 2025

Submission Date

July 3, 2025

Acceptance Date

September 28, 2025

Published in Issue

Year 2025 Number: 52

DOI

https://doi.org/10.53570/jnt.1733901

IZ

https://izlik.org/JA98YB66LU

Cite

RIS / Bibtex

APA

Çelik, E. (2025). A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow. Journal of New Theory, 52, 38-51. https://doi.org/10.53570/jnt.1733901

AMA

1.Çelik E. A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow. JNT. 2025;(52):38-51. doi:10.53570/jnt.1733901

Chicago

Çelik, Ebutalib. 2025. “A Hybrid Finite Difference-RBF Method With Polynomial Approach and an Application to MHD Flow”. Journal of New Theory, nos. 52: 38-51. https://doi.org/10.53570/jnt.1733901.

EndNote

Çelik E (September 1, 2025) A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow. Journal of New Theory 52 38–51.

IEEE

[1]E. Çelik, “A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow”, JNT, no. 52, pp. 38–51, Sept. 2025, doi: 10.53570/jnt.1733901.

ISNAD

Çelik, Ebutalib. “A Hybrid Finite Difference-RBF Method With Polynomial Approach and an Application to MHD Flow”. Journal of New Theory. 52 (September 1, 2025): 38-51. https://doi.org/10.53570/jnt.1733901.

JAMA

1.Çelik E. A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow. JNT. 2025;:38–51.

MLA

Çelik, Ebutalib. “A Hybrid Finite Difference-RBF Method With Polynomial Approach and an Application to MHD Flow”. Journal of New Theory, no. 52, Sept. 2025, pp. 38-51, doi:10.53570/jnt.1733901.

Vancouver

1.Ebutalib Çelik. A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow. JNT. 2025 Sep. 1;(52):38-51. doi:10.53570/jnt.1733901