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2nd order upwind scheme (Fluent and CFX)

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Old   May 22, 2011, 01:50
Default 2nd order upwind scheme (Fluent and CFX)
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It is stated in the CFX theory (above link) that when one selects the high resolution scheme as below


\nabla\phi\ is the value at the upwind node.

On the other hand when user selects the specified blend factor for \beta (between 0 and 1), \nabla\phi\ is equal to the average of the adjacent nodal gradients. I wanna know, this scheme is the upwind or central differencing scheme?

Where as in fluent user guide (above link) 2nd order upwind scheme is given by following formula


\nabla\phi\ is the gradient of \phi\ in the upwind cell

Both high resolution (CFX) and 2nd order upwind scheme (Fluent) are based on the principles by Barth and Jespersen [1] so that no new extrema is introduced in the solution, therfore monotonic behavior is preserved.

1. Does it mean that the high resolution scheme of CFX and 2nd order upwind scheme of fluent are equivalent.

2. Does it mean that the CFX 2nd order scheme is more like a baised 2nd order scheme with one term of upwind and 2nd term (anti diffusive term) is central differencing type?

3. Will 2nd order upwind (CFX definition) will make the solution worst than even 1st order upwind scheme?

Barth and Jespersen "The design and application of upwind schemes on unstructured meshes" .
Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.

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