首页|The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid

The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid

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In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O((τ)2+N-r),where(τ) is the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.

fractional MHD coupled flow and heat transfer modelgeneralized second-grade fluidfast methodconvergence analysisnumerical simulation

Xiaoqing Chi、Hui Zhang、Xiaoyun Jiang

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School of Mathematics and Statistics,Shandong University,Weihai 264209,China

School of Mathematics,Shandong University,Jinan 250100,China

Project of the National Key Research and Development Program国家自然科学基金国家自然科学基金国家自然科学基金山东省自然科学基金山东省自然科学基金山东省自然科学基金中国博士后科学基金中国博士后科学基金Startup Fund from Shandong University

2021YFA1000202121201010011200132612171283ZR2021ZD03ZR2020QA032ZR2019ZD42BX201901912020M67203811140082063130

2024

10.1007/s11425-021-2063-0

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(4)
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