[1]张 俊.分数阶黏性方程MHD流的数值方法[J].四川师范大学学报(自然科学版),2019,(05):654-658.[doi:10.3969/j.issn.1001-8395.2019.05.013]
 ZHANG Jun.Numerical Method for MHD Flows of Fractional Viscous Equation[J].Journal of SichuanNormal University,2019,(05):654-658.[doi:10.3969/j.issn.1001-8395.2019.05.013]
点击复制

分数阶黏性方程MHD流的数值方法()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
654-658
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
Numerical Method for MHD Flows of Fractional Viscous Equation
文章编号:
1001-8395(2019)05-0654-05
作者:
张 俊
贵州财经大学 数统学院, 贵州 贵阳 550025
Author(s):
ZHANG Jun
School of Mathematics and Statistical, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou
关键词:
MHD流 谱方法 稳定性 误差估计
Keywords:
MHD flow spectral method stability error estimate
分类号:
O241.82
DOI:
10.3969/j.issn.1001-8395.2019.05.013
文献标志码:
A
摘要:
主要讨论分数阶黏性MHD方程的数值近似.提出一种求解该方程高效的数值格式,分析这种数值格式的稳定性与误差估计,证明这种格式是无条件稳定的,且格式在时间方向是2-β阶精度,在空间方向有谱精度,最后用数值实例验证理论的正确性.
Abstract:
In this paper, the numerical approximation of fractional viscosity MHD equation is discussed.We present an efficient numerical scheme for solving this equation and analyze its stability and error estimates.We prove that the scheme is unconditionally stable and the convergence order of the scheme is time and spectral accuracy in space.Finally, numerical examples are given to verify the theoretical results.

参考文献/References:

[1] PRIEST E R.Solar Magnetohydrodynamic[M].Dordrecht:Reidel,1982.
[2] BISKAMP D.Magnetic Reconnection in Plasmas[M].Cambridge:Cambridge University Press,2000.
[3] BISKAMP D.Magnetohydrodynamic Turbulence[M].Cambridge:Cambridge University Press,2003.
[4] KHAN M, HAYAT T, ASGHAR S.Exact solution for MHD flow of generalized oldroyd-B fluid with modified Darcy's law[J].Int J Eng Sci,2006,4(5/6):333-339.
[5] RIVLIN R S, ERICKSEN J L.Periodic flows of a non-Newtonian fluid between two parallel plates[J].J Rational Mech Anal,1955,4:323-425.
[6] SIDDIQUI A M, HAYAT T, ASGHAR S.Periodic flows of non-Newtonian fluid between two parallel plates[J].Int J Non-Linear Mech,1999,34(5):895-899.
[7] PALADE L I, ATTANE P, HUILGOL R R, et al.Anomalous stability behavior of a properly invariant constitutive equation which generalizes fractional derivative models[J].Int J Eng Sci,1999,37(3):315-329.
[8] ROSSIHIN Y A, SHITIKOVA M V.A new method for solving dynamic problems of fractional derivative viscoelasticity[J].Int J Eng Sci,2001,39(2):149-176.
[9] TAN W C, XU M Y.The impulsive motion of flat plate in a generalized second grade fluid[J].Mech Res Commun,2002,29:3-9.
[10] LIN Y M, Xu C J.Finite difference/spectral approximations for the time-fractional diffusion equation[J].J Comput Phys,2007,225(2):1533-1552.
[11] KHISMATULLIN D, RENARDY Y, RENARDY M.Development and implementation of VOF-PROST for 3D viscoelastic liquid-liquid simulations[J].J Non-Newton Fluid Mech,2006,140(1):120-131.

相似文献/References:

[1]付强.环空内非牛顿流体依时性Couette流动的谱法研究[J].四川师范大学学报(自然科学版),2010,(06):808.
 FU Qiang.Spectral Method for Research on Time Dependent Couette Flowof NonNewtonian Fluid in Ring Sleeve[J].Journal of SichuanNormal University,2010,(05):808.
[2]付强.管内上随体Maxwell流体非定常流动的谱方法研究[J].四川师范大学学报(自然科学版),2003,(04):379.
 FU Qiang (Department of Physics,Southwest University for Nationalities,Chengdu 00,et al.[J].Journal of SichuanNormal University,2003,(05):379.

备注/Memo

备注/Memo:
收稿日期:2017-10-29 接受日期:2018-12-07
基金项目:贵州省科学技术基金(黔科合基础[2019]1051)和贵州省教育厅青年人才项目(黔教合KY字[2018]153)
作者简介:张 俊(1984—),男,博士,副教授,主要从事计算数学的研究,E-mail:zj654440@163.com
更新日期/Last Update: 2019-07-15