Dimension Splitting Method for the Three Dimensional Rotating Navier-Stokes Equations
查看参考文献16篇
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文摘
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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. |
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来源
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Acta Mathematicae Applicatae Sinica-English Series
,2012,28(3):417-442 【核心库】
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DOI
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10.1007/s10255-012-0161-7
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关键词
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stream layer
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2D manifold
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Navier-Stokes equations
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dimension splitting method
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finite element method
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地址
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1.
College of Sciences, Xi’an Jiaotong University, Xi’an, 710049
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Laboratory for Engineering and Scientific Computing, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055
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语种
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英文 |
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ISSN
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0168-9673 |
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学科
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数学 |
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基金
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国家863计划
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国家自然科学基金
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the Foundation of AVIC Chengdu Aircraft Design and Research Institute
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文献收藏号
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CSCD:4622823
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