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A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem. (English) Zbl 1242.76363
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.
MSC:
76W05Magnetohydrodynamics and electrohydrodynamics
76M22Spectral methods (fluid mechanics)
76M25Other numerical methods (fluid mechanics)
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 · doi:10.1093/qjmam/14.3.335
[2]Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A.: Spectral methods in fluid dynamics, (1988) · 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 · doi:10.1016/j.physleta.2008.02.006
[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 · doi:10.1016/j.cnsns.2007.07.009
[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)
[6]Goldstein, S.: Modern developments in fluid dynamics, (1938)
[7]He, J. H.: Variational iteration method: a kind of non-linear analytical technique: some examples, Int J non-linear mech 34, No. 4, 699-708 (1999)
[8]He, J. H.: Variational iteration method for autonomous ordinary differential systems, Appl math comput 114, No. 2-3, 11523 (2000) · Zbl 1027.34009 · doi:10.1016/S0096-3003(99)00104-6
[9]He, J. H.: Homotopy perturbation technique, Comput methods appl mech eng 178, 257-262 (1999)
[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 · doi:10.1016/S0020-7462(98)00085-7
[11]Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis. Shanghai Jiao Tong University; 1992.
[12]Liao, S. J.: Beyond perturbation: introduction to homotopy analysis method, (2003)
[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 · doi:10.1016/j.amc.2004.10.058
[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 · doi:10.1016/j.cnsns.2008.04.013
[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 · doi:10.1016/j.cnsns.2009.02.016
[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 · doi:10.1016/j.cpc.2009.06.006
[17]Makinde, O. D.; Mhone, P. Y.: Hermite – Padé approximation approach to MHD Jeffery – Hamel flows, Appl math comput 181, 966-972 (2006) · Zbl 1102.76049 · doi:10.1016/j.amc.2006.02.018
[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, No. 6, 697-707 (2008) · Zbl 1231.76353 · doi:10.1108/09615530810885524
[19]Makinde, O. D.; Mhone, P. Y.: Temporal stability of small disturbances in MHD Jeffery – Hamel flows, Comput math appl 53, No. 1, 128-136 (2007) · Zbl 1175.76061 · doi:10.1016/j.camwa.2006.06.014
[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 · doi:10.1016/j.cnsns.2009.09.019
[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 · doi:10.1016/S0169-5983(97)00049-X
[22]Reza MS. Channel entrance flow. PhD thesis. Department of Mechanical Engineering, University of Western Ontario; 1997.
[23]Rosenhead, L.: The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc roy soc A 175, No. 963, 43667 (1940) · Zbl 0025.37501 · doi:10.1098/rspa.1940.0068
[24]Trefethen, L. N.: Spectral methods in Matlab, (2000)