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
MHD flow, domain decomposition, radial basis function, single lid L-shaped
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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