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

作　　者：Xiaoqing Chi Hui Zhang Xiaoyun Jiang 

机构地区：[1]School of Mathematics and Statistics,Shandong University,Weihai 264209,China [2]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Science China Mathematics》2024年第4期919-950,共32页中国科学（数学）（英文版）

基　　金：supported by the Project of the National Key R&D Program(Grant No.2021YFA1000202);National Natural Science Foundation of China(Grant Nos.12120101001,12001326 and 12171283);Natural Science Foundation of Shandong Province(Grant Nos.ZR2021ZD03,ZR2020QA032 and ZR2019ZD42);China Postdoctoral Science Foundation(Grant Nos.BX20190191 and 2020M672038);the Startup Fund from Shandong University(Grant No.11140082063130)。

摘　　要：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),whereτis 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.

关 键 词：fractional MHD coupled flow and heat transfer model generalized second-grade fuid fast method convergence analysis numerical simulation 

分 类 号：O361.3[理学—流体力学]