CFD: Non-uniform grid mesh for 2D Rectangular - Fortran code

Result:

Here's part of the code I used to generate a non-uniform grid using fortran. To understand meaning of exp_x & exp_y powers, you need a piece of paper to sketch and calculate it by yourself.

exp_x=1.05 !x-axis expansion factor
exp_y=1.10 !y-axis expansion factor

a=0.
b=1.
c=0.
d=1.

!***********************************

! Constructing non-uniform grid !

!***********************************

! del_x & del_y : Uniform step size in X & Y direction

! eta_x & eta_y : First non-uniform step size in X & Y direction

! i_th step size is : eta_x*expansion_factor^step

del_x=(b-a)/n_x

del_y=(d-c)/n_y

eta_x=(b-a)*(1-exp_x)/(2*(1-exp_x**(n_x/2)))

eta_y=(d-c)*(1-exp_y)/(2*(1-exp_y**(n_y/2)))

PRINT *, "Uniform X-Step:", del_x

PRINT *, "Uniform Y-Step:", del_y

PRINT *, "First Non-uniform X-Step:", eta_x

PRINT *, "First Non-uniform Y-Step:", eta_y

x(1)=a

y(1)=c

! X_START to Middle_X

DO i=2,n_x/2+1

       x(i)=x(i-1)+eta_x*exp_x**(i-2)

END DO

! Middle_X to End

DO i=n_x/2+2,n_x+1

       x(i)=x(i-1)+eta_x*exp_x**(n_x+1-i)

END DO

! Y_START to Middle_Y

DO j=2,n_y/2+1

       y(j)=y(j-1)+eta_y*exp_y**(j-2)

END DO

! Middle_Y to Y_END

DO j=n_y/2+2,n_y+1

       y(j)=y(j-1)+eta_y*exp_y**(n_y+1-j)

END DO

!***********************************

! non-uniform grid done !

!***********************************