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The Boundary Layer Equations and a Dimensional Split Method for Navier-Stokes Equations in Exterior Domain of a Spheroid and Ellipsoid
School of Mathematics and Statistic, Xi’an Jiaotong University, Xi’an, China
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China
School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China
School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China
- 1 School of Mathematics and Statistic, Xi’an Jiaotong University, Xi’an, China
- 2 School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China
- 3 School of Computer Engineering and Science, Shanghai University, Shanghai, China
- 4 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China
- 5 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China
International Journal of Modern Nonlinear Theory and Application·Volume 04 (2015)·Pages 48–87·Published 16 February 2015·DOI10.4236/ijmnta.2015.41005
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Abstract
In this paper, the boundary layer equations (abbreviation BLE) for exterior flow around an obstacle are established using semi-geodesic coordinate system ( S -coordinate) based on the curved two dimensional surface of the obstacle. BLE are nonlinear partial differential equations on unknown normal viscous stress tensor and pressure on the obstacle and the existence of solution of BLE is proved. In addition a dimensional split method for dimensional three Navier-Stokes equations is established by applying several 2D-3C partial differential equations on two dimensional manifolds to approach 3D Navier-Stokes equations. The examples for the exterior flow around spheroid and ellipsoid are presents here.
KeywordsBoundary Layer EquationsDimensional Split MethodNavier-Stokes EquationsDimensional Two Manifold
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