Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations

Selçuk Han Aydın; Alpha Peter Lukonde

doi:10.31801/cfsuasmas.1696392

Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations

Abstract

In this study, the solution of the steady magnetohydrodynamic (MHD) equations is considered on various 2D and 3D closed domains (triangle, tetrahedron, pyramid and conic) and channel configurations such as swollen channel, collapsed channel, narrowed channel and wrinkled curved channel which are encountered in many real-life applications. As a numerical procedure both stabilized finite element method (FEM) and coupled dual reciprocity boundary element method (DRBEM) formulation are used. The coupled DRBEM is different from the previous literature on decoupled DRBEM, and it enables the use of different boundary condition types that are proposed for the moderate and high Hartmann number values. The other benefit of coupled DRBEM is that it combines all the coefficients of the unknown variables including the normal derivatives into a single coefficient matrix, therefore in one computation stroke one finds the solution to the problem. The wrinkled curved channel flow may be applied to the analysis of blood flow under the influence of an externally applied magnetic field in the stenosed artery. Some numerical calculations were performed for the different problem parameters and boundary conditions. The comparison of the results for some test problems using the proposed numerical schemes are presented in tables and contour plots.

Keywords

Supporting Institution

No any support

Thanks

The authors wish to thank Prof.Dr. M. Tezer-Sezgin for her valuable support, comments and suggestions.

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Details

Primary Language

English

Subjects

Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Selçuk Han Aydın ^*
0000-0002-1419-9458
Türkiye

Alpha Peter Lukonde
0000-0001-6813-4505
Türkiye

Publication Date

March 29, 2026

Submission Date

May 9, 2025

Acceptance Date

July 20, 2025

Published in Issue

Year 2026 Volume: 75 Number: 1

DOI

https://doi.org/10.31801/cfsuasmas.1696392

IZ

https://izlik.org/JA92SZ72DL

Cite

RIS / Bibtex

APA

Aydın, S. H., & Lukonde, A. P. (2026). Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 75(1), 38-56. https://doi.org/10.31801/cfsuasmas.1696392

AMA

1.Aydın SH, Lukonde AP. Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75(1):38-56. doi:10.31801/cfsuasmas.1696392

Chicago

Aydın, Selçuk Han, and Alpha Peter Lukonde. 2026. “Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 (1): 38-56. https://doi.org/10.31801/cfsuasmas.1696392.

EndNote

Aydın SH, Lukonde AP (March 1, 2026) Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 1 38–56.

IEEE

[1]S. H. Aydın and A. P. Lukonde, “Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 75, no. 1, pp. 38–56, Mar. 2026, doi: 10.31801/cfsuasmas.1696392.

ISNAD

Aydın, Selçuk Han - Lukonde, Alpha Peter. “Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75/1 (March 1, 2026): 38-56. https://doi.org/10.31801/cfsuasmas.1696392.

JAMA

1.Aydın SH, Lukonde AP. Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75:38–56.

MLA

Aydın, Selçuk Han, and Alpha Peter Lukonde. “Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 75, no. 1, Mar. 2026, pp. 38-56, doi:10.31801/cfsuasmas.1696392.

Vancouver

1.Selçuk Han Aydın, Alpha Peter Lukonde. Visualizing Stabilized FEM and Coupled DRBEM Solutions of MHD Equations in Different Channel Configurations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Mar. 1;75(1):38-56. doi:10.31801/cfsuasmas.1696392