Navier-Stokes方程的球坐标列矢量变换

Vector Transform of Spherical Coordinate Form of Navier-Stokes Equation

流体力学中Navier-Stokes方程的坐标表示一般都比较复杂,计算过程十分烦琐,因此众多的书刊上都没有求解过程.本文利用过渡矩阵,先把Navier-Stokes方程中的粘滞应力张量由笛卡儿坐标系变换到球坐标系,然后对Navier-Stokes方程进行球坐标列矢量变换.推导结果和经典方法相同,证明了此方法的正确性.

It is very complex to figure the spherical coordinate form of Navier-Stokes equation in fluid mechanics, so there are no solution process in many books and periodicals. Puts forward a simple method using the transitional matrix. Firstly transforms Cartesian coordinates of stress tensor, which in Navier-Stokes equation, to spherical coordinate, then does vector transform of spherical coordinate to Navier-Stokes equation. The results are the same comparing with the classical method.