Nonlinear Spectral Analysis in a Multiply-Connected Region

多重连通区域中的非线性谱分析

• 批准号: 17540104
• 负责人: MOCHIMARU Yoshihiro
• 金额: $ 2.2万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540104/
• 关键词: Spectral finite difference; Multiply-connected; Compatibility; Natural convection

The spectral difference scheme is very effective to numerical analysis for nonlinear partial differential equations, such as Navier-Stokes equations. Effectiveness has been extended, using a conformal mapping with doubly-periodic functions.Target equations are mainly partial differential equations with boundary values and/or initial values.In this project, triply-connected two-dimensional regions or axisymmetric doubly-connected regions are treated. At the first stage, fluid is assumed to be Newtonian.(i) Various conformal mapping function are introduced.(ii) Various configurations are treated.(iii) Region of infinite extension, non-isothermal boundary, and natural convection is treated.As a result, conformal mapping using Jacobian elliptic functions is found to be very effective in multiply-connected region under a spectral finite difference scheme.

谱差分格式是求解非线性偏微分方程，如Navier-Stokes方程的一种非常有效的方法。本文利用双周期函数的保角变换，将问题的有效性加以扩展，目标方程主要是带边值和/或初值的偏微分方程，本文处理的是三维连通区域或轴对称双连通区域。在第一阶段，假设流体是牛顿流体。(i)介绍了各种保角映射函数。(ii)处理各种配置。(iii)讨论了无限延伸、非等温边界和自然对流区域，结果表明，在谱差分格式下，利用Jacobian椭圆函数的保角变换在多连通区域是非常有效的。

项目成果

Spectral Analysis on Natural Convection Heat Transfer from a Rectangular Cylinder Partially Heated in an Infinite Extension

无限延伸部分加热的矩形圆柱体自然对流换热的谱分析

• 发表时间: 2008
• 期刊: International Journal of Pure and Applied Mathematics 44(In press)
• 作者: 山本 野人;小森 喬;足立 英輔;N.Yamamoto;N.Yamamoto;N.Yamamoto;Yoshihiro Mochimaru & Myung-whan Bae
• 通讯作者: Yoshihiro Mochimaru & Myung-whan Bae

Application of Conformal Maw. to Heat Transfer Analysis

保形胃的应用。

• 发表时间: 2007
• 期刊: Proc. 10th International Symposium on Technology for Next Generation Vehicle & Machine
• 作者: Yoshihiro;Mochimaru;Myung-whan.;Bae
• 通讯作者: Bae

Natural Convection Heat Transfer in a Doubly-Connected Region, using a Spectral Finite Difference Scheme

使用谱有限差分格式的双连接区域中的自然对流换热

• 发表时间: 2006
• 期刊: Third International Conference of Applied Mahematics 2
• 作者: Yoshihiro Mochimaru;Myung-whan Bae;Yoshihiro Mochimaru & Myung-whan BAE;Yoshihiro Mochimaru & M-W. Bae
• 通讯作者: Yoshihiro Mochimaru & M-W. Bae

Solution of Sextic Equations

六次方程的解

• 发表时间: 2005
• 期刊: Second International Conference of Applied Mathematics 2
• 作者: Y.Mochimaru;M-W;Bae;Yoshihiro Mochimaru
• 通讯作者: Yoshihiro Mochimaru