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Dimension Splitting Method for the Three Dimensional Rotating Navier-Stokes Equations

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Li Kaitai 1 *   Yu Jiaping 1   Shi Feng 2   Huang Aixiang 1  
文摘 In this paper, we propose a dimensional splitting method for the three dimensional (3D) rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces T_i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate (S-coordinate) system based on T_i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on T_i, another one is called the bending operator taking value in the normal space on T_i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface T_i is obtained, which is called the two-dimensional three-component (2D-3C) Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stokes equations are presented.
来源 Acta Mathematicae Applicatae Sinica-English Series ,2012,28(3):417-442 【核心库】
DOI 10.1007/s10255-012-0161-7
关键词 stream layer ; 2D manifold ; Navier-Stokes equations ; dimension splitting method ; finite element method
地址

1. College of Sciences, Xi’an Jiaotong University, Xi’an, 710049  

2. Laboratory for Engineering and Scientific Computing, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055

语种 英文
ISSN 0168-9673
学科 数学
基金 国家863计划 ;  国家自然科学基金 ;  the Foundation of AVIC Chengdu Aircraft Design and Research Institute
文献收藏号 CSCD:4622823

参考文献 共 16 共1页

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