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References (18)
-
Wenyi Chen, J. Jost (2002)
A Riemannian version of Korn's inequalityCalculus of Variations and Partial Differential Equations, 14
-
P. Ciarlet (2006)
An Introduction to Differential Geometry with Applications to ElasticityJournal of Elasticity, 78-79
-
(1992)
Parallel finite element methods -
李开泰, 黄艾香 (2002)
THE NAVIER-STOKES EQUATIONS IN STREAM LAYER AND ON STREAM SURFACE AND A DIMENSION SPLIT METHODS -
(2000)
Mathematical elasticity, Vol. III: Theory of shells, Series “Studies in Mathematics and Its Applications -
(1992)
Domain Decomposition Methods–New Numerical Techniques for Solving PDE -
Kaitai Li, Demin Liu
International Journal of C 2009 Institute for Scientific Numerical Analysis and Modeling Computing and Information Dimension Splitting Method for 3d Rotating Compressible Navier-stokes Equations in the Turbomachinery -
T. Bratanow (1978)
Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00Applied Mathematical Modelling, 2
-
(2000)
Tensor analysis and its applications -
V. Girault, P. Raviart (1986)
Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms, 5
-
R. Temam (1984)
Navier-Stokes Equations: Theory and numerical analysis -
L. Kaitai, H. Aixiang (1983)
Mathematical aspect of the stream-function equations of compressible turbomachinery flows and their finite element approximations using optimal controlComputer Methods in Applied Mechanics and Engineering, 41
-
D. Ebin, J. Marsden (1970)
Groups of diffeomorphisms and the motion of an incompressible fluidAnnals of Mathematics, 92
-
K.T. Li, D.M. Liu (2009)
Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the TurbomachineryInternational Journal of Numerical Analysis and Modeling, 6
-
K.T. Li, H.L. Jia (2008)
The Navier Stokes Equations on the Stream surface and its Dimension Splitting MethodActa Mathematica Scientia, 2
-
Kaitai Li, Xiaoqin Shen (2007)
A dimensional splitting method for the linearly elastic shellInternational Journal of Computer Mathematics, 84
-
Kaitai Li, A. Huang, W. Zhang (2001)
A dimension split method for the 3‐D compressible Navier–Stokes equations in turbomachineCommunications in Numerical Methods in Engineering, 18
-
A. Il’in (1991)
THE NAVIER-STOKES AND EULER EQUATIONS ON TWO-DIMENSIONAL CLOSED MANIFOLDSMathematics of The Ussr-sbornik, 69
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Math Applications in Computer Science
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-012-0161-7
- Publisher site
- See Article on Publisher Site
Abstract
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 $\Im $ and is decomposed by a series of surfaces $\Im _i $ into several sub-domains, which are called the layers of the flow. Every interface $\Im _i $ between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate (S-coordinate) system based on $\Im _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 $\Im _i $ , another one is called the bending operator taking value in the normal space on $\Im _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 $\Im _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.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jun 10, 2012