The Boundary Layer Equations and a Dimensional Split Method for Navier-Stokes Equations in Exterior Domain of a Spheroid and Ellipsoid

Jian Su¹, Hongzhou Fan², Weibing Feng³, Hao Chen⁴, Kaitai Li^1*

¹School of Mathematics and Statistic, Xi’an Jiaotong University, Xi’an, China.
¹School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China.
²School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China.
³School of Computer Engineering and Science, Shanghai University, Shanghai, China.
⁴School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China.

DOI: 10.4236/ijmnta.2015.41005                

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.

Keywords

Boundary Layer Equations, Dimensional Split Method, Navier-Stokes Equations, Dimensional Two Manifold

Conflicts of Interest

The authors declare no conflicts of interest.

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