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some confusion about the user guide's sentence.

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Old   January 13, 2015, 05:19
Default some confusion about the user guide's sentence.
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Dongyue Li
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Hi guys,

In page 35: it said:

Code:
The error in any solution will be more pronounced in regions where the form of the true solution differ widely from the form assumed in the chosen numerical schemes. For example a numerical scheme based on linear variations of variables over cells can only generate an exact solution if the true solution is itself linear in form. The error is largest in regions where the true solution deviates greatest from linear form, i.e. where the change in gradient is largest. Error decreases with cell size.
Im confused about this true solution and exact solution. are they analytic solution? and are they the same one?

Also what does this "form" means?

Thanks.

Sorry , this link. in sector 2.1.6. http://www.openfoam.org/docs/user/ca...#x5-250002.1.6
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Old   January 13, 2015, 07:05
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Andrea Bianco
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Hi,
The true solution is the analitical solution to n-s equation, applied without discretizing equations or domain. An exact solution is a computed solution equal to the true solution.

Basically the user guide is saying that you have to consider the proper numerical scheme to use and the cell size. Let's consider two cell centroid and let's say we know the analitical solution between them. Let's also say that the centroid values are equal to the solution values for a certain fluid property. If the true solution is not linear between the cell centroids and you are using a linear numerical scheme, then you will obtain a calculated gradient that will be only a rough approximation of the true gradient. So large error are expected. If you decrease the cell size then the computed gradient will better approximate the true gradient, so the error will decrease.

We have to consider that centroid values are influenced by gradient calculation, as per discretized n-s equations...so If we have large error in gradient calculations then we will probably obtain an incorrect solution (not equal to analitical solution)
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