Periodic Boundary Condition for upwind difference
 

Hi,

I am solving 2D compressible inviscid flow by forward difference for time and upwind difference for space.
I must also impose periodic boundary condition.
But how should I treat the condition?

Tentatively, I imposed following one-sided difference,
f_0 = f_N+1
(-3f_0 + 4f_1 - f_2)/dx = (f_N-1 - 4f_N + 3f_N+1)/dx

This condition gets along for a certain initial profile, such as homogeneous temperature.

Otherwise, it diverges near downwind boundary ( j ~ 8 calculating j = 1 to 100 ).

What is correct periodic boundary condition for upwind difference method?

Thanks in advance.