[1]朱玉川,马大为,乐贵高,等.基于坐标变换的球面坐标Navier-Stokes方程的建立[J].南京理工大学学报(自然科学版),2005,(04):437-440.
 ZHU Yu-chuan~,MA Da-wei~,LE Gui-gao~,et al.Foundation of Navier-Stokes Equations in Spherical Coordinates System Based on Coordinate Transformation[J].Journal of Nanjing University of Science and Technology,2005,(04):437-440.
点击复制

基于坐标变换的球面坐标Navier-Stokes方程的建立
分享到:

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
2005年04期
页码:
437-440
栏目:
出版日期:
2005-08-30

文章信息/Info

Title:
Foundation of Navier-Stokes Equations in Spherical Coordinates System Based on Coordinate Transformation
作者:
朱玉川1 马大为1 乐贵高1 徐长江1 2
1.南京理工大学机械工程学院, 江苏南京210094; 2.海军兵种指挥学院三系, 广东广州510430
Author(s):
ZHU Yu-chuan~1MA Da-wei~1LE Gui-gao~1XU Chang-jiang~12
1.School of Mechanical Engineering, NUST, Nanjing 210094,China;2 The Third Department,Guangzhou Naval Arms-commanding Academy,Guangzhou 510430,China)HT6SS
关键词:
Navier-Stokes 方程 坐标变换 笛卡尔坐标 球面坐标
Keywords:
Navier-Stokes equat ions coordinate transformation Cartesian coordinates spherical coordinates
分类号:
O351.2
摘要:
利用笛卡尔坐标系内的Navier-Stokes方程的数学形式,采用坐标变换的方法通过对方程各物理量的数学推导,分别对拉普拉斯算子、质点散度以及质点加速度等进行坐标转换及其简化,建立了完整的球面坐标系内的Navier-Stokes方程。证明了笛卡尔坐标和球面坐标系下Navier-Stokes方程的一致性,并为其他坐标形式的Navier-Stokes方程之间的转换提供了研究参考。
Abstract:
Based on the mathematic expression of Navier-Stokes equations in Cartesian coordinate system, this paper presents a simple method for deriving Navier-Stokes equat ions in spherical coordinate system. Navier-Stokes equations in spherical coordinate system are derived by utilizing a new method by which the coordinate transformation and the simplificat ion of Laplaceian operator, the divergence of particles and the acceleration of particles from Cartesian coordinate system to spherical coordinate system are made. The consistence of Navier-Stokes equations both in Cartesian coordinate system and in spherical coordinate system is proved, and the references for research about the coordinate transformation of Navier-Stokes equations in other coordinate systems are provided.

参考文献/References:

[ 1] 盛敬超. 液压流体力学[M] . 北京: 机械工业出版社, 1980.
[ 2] 市川常雄. 液压技术基本理论[M] . 北京: 煤炭工业出版社, 1975.
[ 3] 同济大学数学教研室. 高等数学[M] . 北京: 高等教育出版社, 1993.
[ 4] 张靖周, 李立国, 吴国钊. 三维曲线坐标系N- S 方程的通用形式和数字解[ J] . 南京航空航天大学学报. 1994, 26( 4) : 471- 476.
[ 5] Menaldi J L, Sr itharan S S. Stochastic 2-D Navier-Stokes equation[ J] . Applied Mathematics Optimization, 2002, 46: 31 - 53.
[ 6] Katz N H, Parlovi N. A cheap Caffarell-i Kohn-Nirenberg inequality for the Navier- Stokes equation with hyper- dissipation [ J] . Geometric and Functional Analysis, 2002, 12: 355- 379.

相似文献/References:

[1]雷沃妮.机载雷达空域稳定算法[J].南京理工大学学报(自然科学版),2005,(02):178.
 LEI Wo-ni.Airspace Stabilization Algorithm for Airborne Radar System[J].Journal of Nanjing University of Science and Technology,2005,(04):178.

备注/Memo

备注/Memo:
作者简介: 朱玉川( 1974- ) , 男, 安徽淮南人, 博士生, 主要研究方向: 机电系统动力学分析与设计, E-mail: ZYC good@ yahoo. com. cn。
更新日期/Last Update: 2013-03-03