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Periodic Boundary Condition for upwind difference

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Old   October 27, 2010, 13:10
Post Periodic Boundary Condition for upwind difference
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Yohei Kawazura
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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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compressible flow, periodic boundary, upwind diffrence

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