Periodic Boundary Condition for upwind difference
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.
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