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Motsa, S. S.; Sibanda, P.; Awad, F. G.; Shateyi, S.

A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem. (English) Zbl 1242.76363

Comput. Fluids 39, No. 7, 1219-1225 (2010).
Summary: In this paper a novel hybrid spectral-homotopy analysis technique and the homotopy analysis method (HAM) are compared through the solution of the nonlinear equation for the MHD Jeffery-Hamel problem. An analytical solution is obtained using the homotopy analysis method (HAM) and compared with the numerical results and those obtained using the new hybrid method. The results show that the spectral-homotopy analysis technique converges at least twice as fast as the standard homotopy analysis method.

Cited in 1 Review
Cited in 52 Documents

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76M22 Spectral methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)

Keywords:

Jeffery-Hamel flow; magnetohydrodynamics; spectral-homotopy analysis method; nonlinear equations

Software:

Matlab
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\textit{S. S. Motsa} et al., Comput. Fluids 39, No. 7, 1219--1225 (2010; Zbl 1242.76363)
Full Text: DOI

References:

[1] Axford, W. I., The magnetohydrodynamic Jeffery-Hamel problem for a weakly conducting fluid, Q J Mech Appl Math, 14, 335-351 (1961) · Zbl 0106.40801
[2] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral methods in fluid dynamics (1988), Springer-Verlag: Springer-Verlag Berlin · Zbl 0658.76001
[3] Esmaili, Q.; Ramiar, A.; Alizadeh, E.; Ganji, D. D., An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method, Phys Lett A, 372, 3434-3439 (2008) · Zbl 1220.76035
[4] Domairry, G.; Mohsenzadeh, A.; Famouri, M., The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow, Commun Nonlinear Sci Numer Simul, 14, 85-95 (2008) · Zbl 1221.76056
[5] Ganji, Z. Z.; Ganji, D. D.; Esmaeilpour, M., Study on nonlinear Jeffery-Hamel flow by He’s semi-analytical methods and comparison with numerical results, Comput Math Appl (2009) · Zbl 1189.65298
[6] Goldstein, S., Modern developments in fluid dynamics (1938), Oxford
[7] He, J. H., Variational iteration method: a kind of non-linear analytical technique: some examples, Int J Non-Linear Mech, 34, 4, 699-708 (1999) · Zbl 1342.34005
[8] He, J. H., Variational iteration method for autonomous ordinary differential systems, Appl Math Comput, 114, 2-3, 11523 (2000)
[9] He, J. H., Homotopy perturbation technique, Comput Methods Appl Mech Eng, 178, 257-262 (1999) · Zbl 0956.70017
[10] He, J. H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int J Non-linear Mech, 35, 37-43 (2000) · Zbl 1068.74618
[12] Liao, S. J., Beyond perturbation: introduction to homotopy analysis method (2003), Chapman & Hall/CRC Press
[13] Liao, S. J., Comparison between the homotopy analysis method and the homotopy perturbation method, Appl Math Comput, 169, 1186-1194 (2005) · Zbl 1082.65534
[14] Liao, S. J., Notes on the homotopy analysis method: some definitions and theores, Commun Nonlinear Sci Numer Simul, 14, 983-997 (2009) · Zbl 1221.65126
[15] Liang, S.; Jeffrey, D. J., Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation, Commun Nonlinear Sci Numer Simul, 14, 4057-4064 (2009) · Zbl 1221.65281
[16] Liang, S.; Jeffrey, D. J., An efficient analytical approach for solving 4th order boundary value problems, Comput Phys Commun, 180, 2034-2040 (2009) · Zbl 1197.65109
[17] Makinde, O. D.; Mhone, P. Y., Hermite-Pade approximation approach to MHD Jeffery-Hamel flows, Appl Math Comput, 181, 966-972 (2006) · Zbl 1102.76049
[18] Makinde, O. D., Effect of arbitrary magnetic Reynolds number on MHD flows in convergent-divergent channels, Int J Numer Methods Heat Fluid Flow, 18, 6, 697-707 (2008) · Zbl 1231.76353
[19] Makinde, O. D.; Mhone, P. Y., Temporal stability of small disturbances in MHD Jeffery-Hamel flows, Comput Math Appl, 53, 1, 128-136 (2007) · Zbl 1175.76061
[20] Motsa, S. S.; Sibanda, P.; Shateyi, S., A new spectral-homotopy analysis method for solving a nonlinear second order BVP, Commun Nonlinear Sci Numer Simulat, 15, 2293-2302 (2010) · Zbl 1222.65090
[21] McAlpine, A.; Drazin, P. G., On the spatio-temporal development of small perturbations of Jeffery-Hamel flows, Fluid Dyn Res, 22, 123-138 (1998) · Zbl 1051.76554
[23] Rosenhead, L., The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc Roy Soc A, 175, 963, 43667 (1940) · JFM 66.1385.02
[24] Trefethen, L. N., Spectral methods in MATLAB (2000), SIAM · Zbl 0953.68643
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