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9 point laplacian

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Old   November 25, 2011, 20:10
Default 9 point laplacian
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valerio
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Goodmorning,
I'm trying to solve a PDE (ex: dT/dt=Lapl(T)) and I would try to access the 8 points close to a cell "i" in order to calculate a 9 point laplacian.
The idea it's to solve it in a esplicit way using a forAll loop on the internal mesh points of the domain.
The mesh is regular and the domain is a square (nothing complicated).
Can you please tell me, once that I start the farAll loop how to find the neighboors of (exemple) alpha[i]? and how they are ordered (N,S,E,W,NE,NW,SW and SE)?
thank you

Last edited by Alucard; November 26, 2011 at 03:59.
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Old   November 26, 2011, 02:48
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ngj
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Niels Gjoel Jacobsen
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Hello and good morning to you

1. You can get all of the neighbours including the cell, cellI, itself by using the following:

Code:
const labelListList & cellPoints( mesh.cellPoints() );
const labelListList & pointCells( mesh.pointCells() );

label count(0);
const labelList & cps( cellPoints[cellI] );

forAll(cps, pointi)
    count += pointCells[cps[pointi]].size();

labelList allCellCells(count);
count = 0;

forAll(cps, pointi)
{
const labelList & pcs( pointCells[cellPoints[cellI]] );
forAll( pcs, celli)
allCellCells[count++] = pcs[celli];
}

// Do a sort and a unique to remove duplicates
2. You cannot be ensured any particular ordering at all, as the underlying mesh structure in OF is unstructured.

Good luck,

Niels
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Old   November 28, 2011, 06:17
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valerio
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Thank you very much i try it (infact i solve a more complicated equation than the heat transfer one but I needed the 9 points stencil so your answer is really what I need)
--
Best regards,
Valerio
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Old   November 28, 2011, 06:28
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ngj
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Niels Gjoel Jacobsen
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Hi Valerio

Good. BTW: Note that the outlined code also works in 3D, which would give you the entire 27 cell stencil.

I typically use the std::sort and std::unique to truncate the list of cell labels.

Best regards,

Niels
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