Science China-Mathematics最新文献_第5页

The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid 广义二级流体分式磁流体动力耦合流动传热模型的快速方法及收敛性分析

2区数学

Science China-Mathematics Pub Date : 2023-06-19 DOI: 10.1007/s11425-021-2063-0

Xiaoqing Chi, Hui Zhang, Xiaoyun Jiang

{"title":"The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid","authors":"Xiaoqing Chi, Hui Zhang, Xiaoyun Jiang","doi":"10.1007/s11425-021-2063-0","DOIUrl":"https://doi.org/10.1007/s11425-021-2063-0","url":null,"abstract":"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(τ2 + 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.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135380346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Surjective Lp-isometries on Grassmann spaces Grassmann空间上的满射lp等距

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-14 DOI: 10.1007/s11425-021-2055-5

Wenhua Qian, Junhao Shen, Wei Shi, Wenming Wu, Wei Yuan

引用次数: 0

Splitting positive sets 分裂正集

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-13 DOI: 10.1007/s11425-022-2066-x

Hang Zhang, Jialiang He, Shuguo Zhang

引用次数: 0

Existence, construction and extension of continuous solutions of an iterative equation with multiplication 一类带乘法迭代方程连续解的存在、构造与推广

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-13 DOI: 10.1007/s11425-022-2056-6

C. Gopalakrishna, Murugan Veerapazham, Suyun Wang, Weinian Zhang

引用次数: 1

Nitsche-XFEM for a time fractional diffusion interface problem 时间分数扩散界面问题的Nitsche-XFEM

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-07 DOI: 10.1007/s11425-021-2062-6

Tao Wang, Yanping Chen

引用次数: 0

Twisted Whittaker modules over Uq(gln+1)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${U_q}({mathfrak{g}mathfrak{l Twisted Whittaker模块在Uq(gln+1)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsssy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${U_q}({mathfrak{g}mathfrak{l)

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-07 DOI: 10.1007/s11425-022-2079-3

L. Xia, K. Zhao

引用次数: 0

A geometric characterisation of real C*-algebras 实数C*-代数的几何表征

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-06-07 DOI: 10.1007/s11425-022-2041-8

C. Chu

引用次数: 0

Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds Finsler流形的超连接和一个本征Gauss-Bonnet-Chern公式

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-05-25 DOI: 10.1007/s11425-023-2144-6

Huitao Feng, Ming Li

引用次数: 0

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws 双曲守恒律的无振荡Hermite WENO格式

IF 1.4 2区数学

Science China-Mathematics Pub Date : 2023-05-24 DOI: 10.1007/s11425-022-2064-1

Zhuang Zhao, J. Qiu

引用次数: 0

Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere 高维球面上约束高指数鞍形动力学的离散化及指标鲁棒误差分析

2区数学

Science China-Mathematics Pub Date : 2023-05-15 DOI: 10.1007/s11425-022-2149-2

Lei Zhang, Pingwen Zhang, Xiangcheng Zheng

{"title":"Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere","authors":"Lei Zhang, Pingwen Zhang, Xiangcheng Zheng","doi":"10.1007/s11425-022-2149-2","DOIUrl":"https://doi.org/10.1007/s11425-022-2149-2","url":null,"abstract":"We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensional unit sphere. Compared with the saddle dynamics without constraints, the constrained high-index saddle dynamics has more complex dynamical forms, and additional operations such as the retraction and vector transport are required due to the constraint, which significantly complicate the numerical scheme and the corresponding numerical analysis. Furthermore, as the existing numerical analysis results usually depend on the index of the saddle points implicitly, the proved numerical accuracy may be reduced if the index is high in many applications, which indicates the lack of robustness with respect to the index. To address these issues, we derive the error estimates for numerical discretization of the constrained high-index saddle dynamics on the high-dimensional sphere, and then improve it by providing an index-robust error analysis in an averaged norm by adjusting the relaxation parameters. The developed results provide mathematical supports for the accuracy of numerical computations.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136215922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5