An Effective Numerical Method of the Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid With Fractional Derivative

ZHUANG Ping-hui; LIU Qing-xia

doi:10.3879/j.issn.1000-0887.2009.12.005

Volume 30 Issue 12

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ZHUANG Ping-hui, LIU Qing-xia. An Effective Numerical Method of the Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid With Fractional Derivative[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1440-1452. doi: 10.3879/j.issn.1000-0887.2009.12.005

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An Effective Numerical Method of the Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid With Fractional Derivative

doi: 10.3879/j.issn.1000-0887.2009.12.005

School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China

Received Date: 2008-12-20
Rev Recd Date: 2009-10-10
Publish Date: 2009-12-15

Abstract

Abstract

The Ray leigh-Stokes problem for a heated generalized second grade fluid(RSP-HGSGF) with fractional derivative was considered.An effective numerical method for approximating RSP-HGSGF in a bounded domain was presented.And the stability and conver gence of the numerical method were analyzed.Finally,some numerical examples were presented to show the application of the present technique.
- Rayleigh-Stokes problem,
- numerical method,
- stability,
- convergence

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References(17)

References

[1]	Rajagopal K R.On the decay of vortices in a second grade fluid[J].Meccanica,1980,15（3）:185-188. doi: 10.1007/BF02128929
[2]	Rajagopal K R,Gupta A S.On a class of exact solutions to the equations of motion of a second grade fluid[J].International Journal of Engineering Science,1981,19（7）:1009-1014. doi: 10.1016/0020-7225(81)90135-X
[3]	Rajagopal K R.A note on unsteady unidirectional flows of a non-Newtonian fluid[J].Int J Non-Linear Mech,1982,17（5/6）:369-373. doi: 10.1016/0020-7462(82)90006-3
[4]	Bandelli R,Rajagopal K R.Start-up flows of second grade fluids in domains with one finite dimension[J].Int J Non-Linear Mech,1995,30(6):817-839. doi: 10.1016/0020-7462(95)00035-6
[5]	Fetecau C,Zierep J.On a class of exact solutions of the equations of motion of a second grade fluid[J].Acta Mech, 2001,150(1/2):135-138. doi: 10.1007/BF01178551
[6]	Taipel I.The impulsive motion of a flat plate in a visco-elastic fluid[J].Acta Mech,1981,39:277-279. doi: 10.1007/BF01170349
[7]	Zierep J,Fetecau C.Energetic balance for the Rayleigh-Stokes problem of a Maxwell fluid[J].International Journal of Engineering Science,2007,45(2/8):617-627. doi: 10.1016/j.ijengsci.2007.04.015
[8]	SHEN Fang,TAN Wen-chang,ZHAO Yao-hua,et al. The Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model[J].Nonlinear Anaylysis:Real World Applications, 2006,7(5):1072-1080. doi: 10.1016/j.nonrwa.2005.09.007
[9]	XUE Chang-feng,NIE Jun-xiang.Exact solutions of the Rayleigh-Stokes problem for a heated generalized second grade fluid in a porous half-space[J].Applied Mathematical Modelling,2009,33(1):524-531. doi: 10.1016/j.apm.2007.11.015
[10]	Liu F,Anh Y,Turner I.Numerical solution of the space fractional Fokker-Planck equation[J].J Comp Appl Math,2004,166(1):209-219. doi: 10.1016/j.cam.2003.09.028
[11]	Liu F,Anh V,Turner I,et al.Numerical solution for the solute transport in fractal porous media[J].ANZIAM J(E),2004,45:461-473.
[12]	Shen S,Liu F.Error analysis of an explicit finite difference approximation for the space fractional diffusion equation with insulated ends[J].ANZIAM J(E),2004,46:871-887.
[13]	Roop J P.Computational aspects of FEM approximation of fractional advection dispersion equation on bounded domains in R2[J].J Comp Appl Math, 2006,193(1):243-268. doi: 10.1016/j.cam.2005.06.005
[14]	CHEN Chang-ming,Liu F,Anh V.Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives[J].Applied Mathematics and Computation,2008,204(1):340-351. doi: 10.1016/j.amc.2008.06.052
[15]	CHEN Chang-ming,Liu F,Anh V.A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative[J].J Comp Appl Math,2009,42(2):333-339.
[16]	WU Chun-hong.Numerical solution for Stokes' first problem for a heated generalized second grade fluid with fractional derivative[J].Appl Nume Math,2009,59(10):2571-2583. doi: 10.1016/j.apnum.2009.05.009
[17]	Samko S G,Kilbas A A,Marichev O I.Fractional Integrals and Derivatives:Theory and Applications[M].New York,NY:Gordon and Breach Science Publishers,1993.