Comparison of FSM and BEM Solutions of MHD Equations

Selçuk Han Aydın; Shokoufeh Ghezeljeh

doi:10.17776/csj.1980388

Comparison of FSM and BEM Solutions of MHD Equations

Abstract

We consider the numerical solutions of the MagnetoHydroDynamic (MHD) equations both in 2D and 3D domains using Fundamental Solution Method (FSM) also known as meshless method and Boundary Element Method (BEM) where both of them uses the fundamental solution of the differential operator. The considered MHD equations are transformed to the convection-diffusion type and modified Helmholtz type forms in order to apply the considered numerical methods. Formulized four different types of numerical schemes are compared with the either the exact solution if possible or with the Finite Element Method (FEM) results for the different Hartmann number values. Obtained solutions are displayed in terms of tables and visualized with figures of the contour plots.

Keywords

FSM, BEM, MHD

Supporting Institution

There is no any financial support for this study.

Ethical Statement

There is no any conflict for the ethical statement.

Thanks

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

References

Shercliff, J. A. (1956). The flow of conducting fluids in circular pipes under transverse magnetic fields. Journal of Fluid Mechanics, 1(6), 644–666.
Dragos, L. (1975). Magnetofluid Dynamics. Abacus Press.
Mazumder, S. (2015). Numerical methods for partial differential equations: Finite difference and finite volume methods. Academic Press.
Johnson, C. (1987). Numerical solution of partial differential equations by the finite element method. Cambridge University Press.
Tezer-Sezgin, M., & Aydın, S. H. (2006). Solution of magnetohydrodynamic flow problems using the boundary element method. Engineering Analysis with Boundary Elements, 30(5), 411–418. https://doi.org/10.1016/j.enganabound.2005.12.001
Tezer-Sezgin, M., & Aydın, S. H. (2013). BEM solution of MHD flow in a pipe coupled with magnetic induction of exterior region. Computing, 95(8), 751–770. https://doi.org/10.1007/s00607-012-0270-4
Aydın, S. H., & Tezer-Sezgin, M. (2014). A DRBEM solution for MHD pipe flow in a conducting medium. Journal of Computational and Applied Mathematics, 259, 720–729. https://doi.org/10.1016/j.cam.2013.05.010
Bozkaya, C., & Tezer-Sezgin, M. (2007). Fundamental solution for coupled magnetohydrodynamic flow equations. Journal of Computational and Applied Mathematics, 203(1), 125–144. https://doi.org/10.1016/j.cam.2006.03.013
Sellier, A., Aydın, S. H., & Tezer-Sezgin, M. (2014). Free-space fundamental solution of a 2D steady slow viscous MHD flow. CMES: Computer Modeling in Engineering & Sciences, 102(5), 393–406. https://doi.org/10.3970/cmes.2014.102.393
Fairweather, G., & Karageorghis, A. (1998). The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9(1), 69–95. https://doi.org/10.1023/A:1018981221740

Jiang, X., Chen, W., & Chen, C. S. (2013). A fast method of fundamental solutions for solving Helmholtz-type equations. International Journal of Computational Methods, 10(2), 1341008. https://doi.org/10.1142/S0219876213410089
Chen, C. S., Jiang, X., Chen, W., & Yao, G. (2015). Fast solution for solving the modified Helmholtz equation with the method of fundamental solutions. Communications in Computational Physics, 17(3), 867–886. https://doi.org/10.4208/cicp.181113.241014a
Smyrlis, Y. S. (2009). Applicability and applications of the method of fundamental solutions. Mathematics of Computation, 78(267), 1399–1434. https://doi.org/10.1090/S0025-5718-09-02191-7
Partridge, P. W., Brebbia, C. A., & Wrobel, L. C. (1992). The dual reciprocity boundary element method. Computational Mechanics Publications.
Fan, C. M., Chen, C. S., & Monroe, J. (2009). The method of fundamental solutions for solving convection-diffusion equations with variable coefficients. Advances in Applied Mathematics and Mechanics, 1(2), 215–230.
Wang, F., Fan, C. M., Zhang, C., & Lin, J. (2020). A localized space-time method of fundamental solutions for diffusion and convection-diffusion problems. Advances in Applied Mathematics and Mechanics, 12(4), 940–958.
Liu, S., Li, P. W., Fan, C. M., & Gu, Y. (2021). Localized method of fundamental solutions for two- and three-dimensional transient convection-diffusion-reaction equations. Engineering Analysis with Boundary Elements, 124(1), 237–244. https://doi.org/10.1016/j.enganabound.2020.12.023
Antunes, P. R. S. (2022). A well-conditioned method of fundamental solutions for Laplace equation. Numerical Algorithms, 91(1), 1381–1405. https://doi.org/10.1007/s11075-022-01306-x
Liu, C. S. (2012). An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation. Engineering Analysis with Boundary Elements, 36(1), 1235–1245. https://doi.org/10.1016/j.enganabound.2012.03.001
Aydın, S. H. (2013). The method of fundamental solutions of MHD pipe flow in an exterior region. BETEQ 2013 Proceedings of the International Conference on Boundary Element and Meshless Techniques, 67–70.
Bozkaya, C., & Tezer-Sezgin, M. (2006). Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme. International Journal for Numerical Methods in Fluids, 51(5), 567–584. https://doi.org/10.1002/fld.1131
Fendoğlu, H., Bozkaya, C., & Tezer-Sezgin, M. (2018). DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations. Engineering Analysis with Boundary Elements, 93, 124–134. https://doi.org/10.1016/j.enganabound.2018.04.011
Fendoğlu, H., Bozkaya, C., & Tezer-Sezgin, M. (2019). MHD flow in a rectangular duct with a perturbed boundary. Computers & Mathematics with Applications, 77(2), 374–388. https://doi.org/10.1016/j.camwa.2018.09.040
Fendoğlu, H., Bozkaya, C., & Tezer-Sezgin, M. (2024). On the BEM solution of convection–diffusion type equations involving variable convective coefficients. Fluid Dynamics Research, 56(3), 035509. https://doi.org/10.1088/1873-7005/ad56c5
Tezer-Sezgin, M., & Bozkaya, C. (2008). Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field. Computational Mechanics, 41(1), 769–775. https://doi.org/10.1007/s00466-006-0139-5
Aydın, S. H., & Erdogan, M. C. (2023). Stabilization in 3-D FEM and solution of the MHD equations. Mathematical Methods in the Applied Sciences, 46(12), 13395–13410. https://doi.org/10.1002/mma.9259

Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

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

Shokoufeh Ghezeljeh
0009-0008-6685-4937
Türkiye

Publication Date

October 27, 2026

Submission Date

June 27, 2026

Acceptance Date

September 18, 2026

Published in Issue

Year 2026 Volume: 47 Number: 5

DOI

https://doi.org/10.17776/csj.1980388

IZ

https://izlik.org/JA76GJ65DW

APA

Aydın, S. H., & Ghezeljeh, S. (2026). Comparison of FSM and BEM Solutions of MHD Equations. Cumhuriyet Science Journal, 47(5), 1001-1009. https://doi.org/10.17776/csj.1980388

AMA

1.Aydın SH, Ghezeljeh S. Comparison of FSM and BEM Solutions of MHD Equations. CSJ. 2026;47(5):1001-1009. doi:10.17776/csj.1980388

Chicago

Aydın, Selçuk Han, and Shokoufeh Ghezeljeh. 2026. “Comparison of FSM and BEM Solutions of MHD Equations”. Cumhuriyet Science Journal 47 (5): 1001-9. https://doi.org/10.17776/csj.1980388.

EndNote

Aydın SH, Ghezeljeh S (October 1, 2026) Comparison of FSM and BEM Solutions of MHD Equations. Cumhuriyet Science Journal 47 5 1001–1009.

IEEE

[1]S. H. Aydın and S. Ghezeljeh, “Comparison of FSM and BEM Solutions of MHD Equations”, CSJ, vol. 47, no. 5, pp. 1001–1009, Oct. 2026, doi: 10.17776/csj.1980388.

ISNAD

Aydın, Selçuk Han - Ghezeljeh, Shokoufeh. “Comparison of FSM and BEM Solutions of MHD Equations”. Cumhuriyet Science Journal 47/5 (October 1, 2026): 1001-1009. https://doi.org/10.17776/csj.1980388.

JAMA

1.Aydın SH, Ghezeljeh S. Comparison of FSM and BEM Solutions of MHD Equations. CSJ. 2026;47:1001–1009.

MLA

Aydın, Selçuk Han, and Shokoufeh Ghezeljeh. “Comparison of FSM and BEM Solutions of MHD Equations”. Cumhuriyet Science Journal, vol. 47, no. 5, Oct. 2026, pp. 1001-9, doi:10.17776/csj.1980388.

Vancouver

1.Selçuk Han Aydın, Shokoufeh Ghezeljeh. Comparison of FSM and BEM Solutions of MHD Equations. CSJ. 2026 Oct. 1;47(5):1001-9. doi:10.17776/csj.1980388

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

Comparison of FSM and BEM Solutions of MHD Equations

Abstract

Keywords

Supporting Institution

Ethical Statement

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite