Numericalmethod of fluid flow in the cylindrical coordinate
 

Hello everyone,
I am working on simulation of fluid flow in the horizontal cylindrical (closed area/adiabatic), in this case the fluid is N2 gas. I try to solve it in 2D of cylindrical coordinate by HSMAC (Highly simplified Marker and Cell) / implicit method using Fortran programming.

The initial condition of my problem is : Pressure is very high (P = 1 MPa) in the left side of cylindrical, the exactly in the center of radius (1 grid), but in the other part is lower ( P = 100 Pa). So that I consider the velocity at that high pressure becomes high. Meanwhile, the others side the velocity are zero. In the same way, the temperature is also high only in that part (T = 5000 K), and it is lower (T = 300 K) in the another side.

My questions are:
1. From the above condition, I consider to neglect the gravity, is it correct or not?
2. Previously, I have already simulated a case for symmetric flow situation in the vertical cylindrical. But, I am still confused for the horizontal cylindrical because it is non-symmetric flow. Do you have any example of numerical solution in the case or any recommendation book that related with horizontal cylindrical??

Hopefully, anyone can help me..thank you very much.