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1st or 2nd order gradients approach?

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Old   September 13, 2014, 09:26
Default 1st or 2nd order gradients approach?
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huang yu
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hi every one
i have written a 3d unstructured(hybrid) NS solver using a cell-centered finite volume method. three methods of green, unweighted-LSQ and weighted LSQ have implemented to calculate the gradients.after a series of tests on a field which i know analytic solutions of gradients, i found

1)Compare the three methods result with analytic one on regular grid, the relatively error were about 1e-13(machine zero is 1e-14 on my system); and on iregualr grid, the relatively error were about 1e-3 to 1e-5. dose this mean my program works right?

2) on regular grid, all the three methods cannot achieve 2nd order accuracy, the green and unweighted-LSQ achieved 1st order and weighted LSQ was more than 1st; and on iregualr grid the green and unweighted-LSQ cannot achieved 1st order and weighted LSQ was 1st order. i am confused because some people said the three method are 1st order and some said they are 2nd order method, and i want to know dose the gradient accuracy less than 2nd order would have any affect on accuracy of spatial discretization, if i use a linear reconstruction of Barth
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Old   September 17, 2014, 15:30
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There is nothing called first order gradient and second order gradient. Gradient is always first order term. Accuracy of gradient calculation would affect the solution.
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Old   September 18, 2014, 08:07
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The gradient accuracy order for an overall second order FV cell-centered code (linear reconstruction) just need to be first. However, it is important that it is first order on any grid. Still, for fully cartesian, uniform, meshes i expect some methods to return a second order accuracy.

How are you handling your boundary conditions? Is it possible that they are not treated consistently for the analytic solution?
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gradient accuracy

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