Calculating mesh centers runs very slowly
There are two things I would try to change:


Is it necessary, that center_x and center_y are 2-dimensional arrays? In your code, the 2nd dimension holds redundant information and should be avoided.
The biggest problem with pure Python (but often the greatest benefit ;) ) is that it is an interpreted language and numerically heavy operations should be handled with library functions. In your case, I would try to exploit numpy's array features and calculate the center as

center_x = 0.5 * (delta_x[:ncol-1] + delta_x[1:])