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3D gradient computation on unstructred Tet Grid

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Old   January 12, 2020, 07:58
Default 3D gradient computation on unstructred Tet Grid
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dear sir:
I compute the gradient of a physical field "T=sin(3x)*cos(3y)" in a 3d cube with unstructued Tet grid. The gradient of T in z direction should be exactly 0. But the results shown that the absolution error are at the order of -3 and -4.
I want to know how to obtain an accurate results in Tet Grdis.
Regadrs
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Old   January 12, 2020, 11:11
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What method are you using and what other methods can you use in alternative?

However, the absolute error means nothing. You need to refine the grid and see how the error goes down. If you already have a 2nd order method there is probably little you can do to improve it on general unstructured grids
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Old   January 12, 2020, 11:50
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Originally Posted by sbaffini View Post
What method are you using and what other methods can you use in alternative?

However, the absolute error means nothing. You need to refine the grid and see how the error goes down. If you already have a 2nd order method there is probably little you can do to improve it on general unstructured grids
Thanks i use least square method. the average error doesn't decrease any more as i refine the mesh.
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Old   January 12, 2020, 11:56
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You should try to define better "average error" as well as the gradient method (weighted or not? Using the normal equations, QR factorization or a numerical solution for the gradient system?), but there seems to be a problem here, as the LSQ method should be first order on arbitrary grids.

Maybe check that the bc are properly taken into account.

I'm assuming you are using a cell centered finite volume framework
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Old   January 12, 2020, 12:44
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Quote:
Originally Posted by sbaffini View Post
You should try to define better "average error" as well as the gradient method (weighted or not? Using the normal equations, QR factorization or a numerical solution for the gradient system?), but there seems to be a problem here, as the LSQ method should be first order on arbitrary grids.

Maybe check that the bc are properly taken into account.

I'm assuming you are using a cell centered finite volume framework
ok,thanks. I have tried to use a prism grid. it can give very accurate results.
Maybe ,3d Tet grid has some limitations.
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Old   January 12, 2020, 12:50
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The weighted least squares method should be first order accurate on a tetrahedral grid.

Of course, we are talking about non pathological, quite regular grids. Otherwise, the method has well known issues in some specific cases (just google it and you will find the papers mentioning it)
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Old   January 12, 2020, 12:55
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This is the first obvious reference on the topic https://www.google.com/url?sa=t&sour...-UZu_RijfOfWtd
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