TY  - JOUR
T1  - A Hybrid Finite Difference-RBF Method with Polynomial Approach and an Application to MHD Flow
AU  - Çelik, Ebutalib
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.53570/jnt.1733901
JF  - Journal of New Theory
JO  - JNT
PB  - Naim ÇAĞMAN
WT  - DergiPark
SN  - 2149-1402
SP  - 38
EP  - 51
IS  - 52
LA  - en
AB  - 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.
KW  - MHD flow
KW  - domain decomposition
KW  - radial basis function
KW  - single lid L-shaped
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UR  - https://doi.org/10.53570/jnt.1733901
L1  - https://dergipark.org.tr/en/download/article-file/5019150
ER  -