To more accurately solve axisymmetric fluid flows with interfaces,Youngs method for axisymmetric coordinate systems is developed.

Based on the value range for Prandtl number suggested by experiments,how different values of Prandtl number affecting the simulated results was studied qualitatively by using a k-ε model under axisymmetric coordinate.

Solving axially symmetrical electrostatic field in cylindrical coordinates;

The Fourier transformations about the azimuthal angle and Hankel transformation about the radial direction have been used to convert the basic equations of elasticity into a non-homogenous first-order ordinary differential equation system in cylindrical coordinates.

Based on SIMPLE algorithm, Navier-Stokes equations under threedimensional cylindrical coordinates were solved by using the special mesh method to eliminate the singularity at the axis, thereby the computation of three-dimensional turbulent fluid flow in cylindrical reactors can be performed on personal computer and the program developed can be applied in many fields.

This paper derives the expression of speed and acceleration in orthogonal curvilinear coordinate by using elementary geometry and infinitesimal calculus knowledge and gave the specific expression in cylindrical coordinate system and spherical coordinate system.