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Old   August 3, 2007, 13:05
Default Theorical question
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Gui
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In the CFX Manual they say that the discretisation of the advection term is as follows :

phi(ip)=phi(up)+beta*dphi*dr

and they say that phi(up) is the value at the upwind node.

I don't really understand what's the upwind node. Cause if the integration points are located at the center of each surface segment surrounding the finite volume, then the nodes are all at equal distance of the integration point.

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Old   August 3, 2007, 13:24
Default Re: Theorical question
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Robin
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upĚwind (┼*p'w─*nd') adverb. In or toward the direction from which the wind blows.
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Old   August 3, 2007, 13:48
Default Re: Theorical question
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Gui
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ok so it's the upwind node is the node that's in the direction of the flow right?
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Old   August 3, 2007, 13:54
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Robin
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Downwind would be in the direction of the flow, upwind is where it came from.

The best way to think of it is that the upwind value at a face is the variable value from the control volume it is coming from. This value is stored at the node, thus the upwind node. The second part of the equation is a correction for the fact that the value is not constant across the control volume. The gradient represents the variation across the control volume and by multiplying the gradient times the vector distance between the node and the face, you get a corrected value for the face.

Beta is a blend factor that is used to locally ensure that the solution stays bounded.

Regards, Robin
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