3D gradient computation on unstructred Tet Grid
 

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

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.

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.

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)

This is the first obvious reference on the topic https://www.google.com/url?sa=t&sour...-UZu_RijfOfWtd