正交曲线坐标系中粘性表达式的新证明方法  

The New Proof Method of Viscosity Term in Orthogonal Curvilinear Coordinate System

作　　者：李佳 孔玮[2] 高军[3] LI Jia;KONG Wei;GAO Jun(Tangshan University,Teaching Department,Tangshan 063000,China;Huaiyin Institute of Technology,Architecture Engineering Department,Jiangsu 223001,China;China Academy of Aerospace Aerodynamics,Aerodynamics Experiments and Engineering Applications Institute,Beijing 100074,China)

机构地区：[1]唐山学院基础教学部,唐山063000 [2]淮阴工学院建筑工程学院,江苏223001 [3]中国航天空气动力技术研究院空气动力实验与工程应用研究所,北京100074

出　　处：《数学的实践与认识》2021年第20期248-254,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11702107,11802297)。

摘　　要：粘性流体力学中粘性项表达式▽·▽u,可以直接展开拉普拉斯算子得到粘性项▽·▽u的表达式,同时利用微分公式▽·▽u=▽(▽·u)-▽×▽×u中的梯度、散度和旋度也可以得到粘性项表达式,但在正交曲线坐标系中两者计算结果在形式上是不同的.基于这个问题,利用基矢量对曲线坐标的导数公式使正交曲线坐标系中微分公式▽·▽u=▽(▽·u)-▽×▽× u两边的形式一致,在证明过程中,用到了导数交换次序和基矢量满足的微分方程两个关系式.In viscous fluid mechanics,the viscosity term expression is ▽·▽u.Through the Laplace operator,the expansion of the will be obtained.At the same time,in the differentiation formulas ▽·▽u=▽(▽·u)-▽×▽×u,the viscosity term will be got by means of gradient,divergence and rotation.But the results are different in the form in orthogonal curvilinear coordinate system.Based on this problem,in this paper,the differentiation formula▽·▽u=▽(▽·u)-▽×▽×u was proved by using the derivative of the base vector to the curvilinear coordinates.And in the process of proof,the derivative exchange order and differential equation of basis vector will be proved and used.

关 键 词：粘性流体力学 正交曲线坐标系 微分公式 导数交换次序 基矢量满足的微分方程 

分 类 号：O357[理学—流体力学]