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June 6, 2006, 05:45 
Hi,
I am trying to implemen

#1 
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kmurphy
Join Date: Mar 2009
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Hi,
I am trying to implement a solver that calculates a scalar potential over two connected regions. At the boundary the scalar potential must be continuous and there is a specified jump in the gradient. This is very similar to the problem discussed in the thread OpenFOAM Message Board: OpenFoam: Running / Solving / CFD: "Heat transfer with solid elements (conduction)" in which a similar two region Laplacian solver was given (conjugateFoam2.tar.gz). However, in that solver the boundary between the two regions was parallel to the xaxis and the problem is one dimensional, while my problem is 2D and the boundary is more general  it is a circle. Hence I used the following code (my two regions are called 'wire' and 'space', and I am imposing the value of the potential from region 'space' to region 'wire' and the gradient information with jump goes in the opposite direction.) label wire_interface = wire_mesh.boundaryMesh().findPatchID("wire_space") ; label space_interface = space_mesh.boundaryMesh().findPatchID("wire_space" ); // create a reference to the gradient in the wire_space patch of region space fixedGradientFvPatchScalarField& space_T_patch = refCast<fixedgradientfvpatchscalarfield>(space_T.b oundaryField()[space_interface ]); scalarField& space_T_patch_gradient = space_T_patch.gradient(); // calculate vector field of unit normals surfaceVectorField unitNormalField = wire_T.mesh().Sf()/wire_T.mesh().magSf(); // calculate condition for the grad of space_T on boundary wire_space // require that grad of space_T is equal to match volVectorField grad_wire_T = fvc::grad(wire_T); volVectorField match = (grad_wire_T  (jumpFactor*R_w.value()*wire_M_w)); scalarField space_T_grad_condition = (match.boundaryField()[wire_interface] & unitNormalField.boundaryField()[wire_interface]); // use grad of potential condition (wire > space) space_T_patch_gradient = space_T_grad_condition; // use potential condition (space > wire) wire_T.boundaryField()[wire_interface] == space_T.boundaryField()[space_interface]; When I run this solver on a simple domain  a 1D problem, in which the boundary between the two regions is parallel to the xaxis  the calculated solution is as expected. However when I apply it to my 2D problem, the solution grows without apparent bound  nearly doubling at every iteration. Any ideas would be appreciated, KM 

June 7, 2006, 10:10 
Hi K.!
I didn't go through

#2 
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Bernhard Gschaider
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Hi K.!
I didn't go through it in detail (and I don't know where exactly in your code this should be corrected), but is it possible, that the other diffeence between your two grids is that in the first case the gridspacing on the left and the right of the boundary is the same while in the second case they differ by a factor of 2? Have you checked the obundary conditons for T for the noninterface boundaries?
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June 7, 2006, 12:08 
Hi Bernhard,
Thanks for the

#3 
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kmurphy
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Hi Bernhard,
Thanks for the reply. I was worried about the boundary between the two meshes, i.e., whether the faces of the corresponding cells on the commom boundary of both meshes were aligned, and so I wrote code to:
However, the cell volumes (or just areas since it is a 2D problem) may well be different on either side of the common boundary of the two meshes. In the 1D case I ran a few experiments with different size cells on either side of the boundary (while keeping the boundary faces aligned). Varying the cell volume on either side of the boundary had no effect so I assumed that this was not the source of the problem. (Bad idea?) If the relative cell volumes did have an effect how do I add a correction for this when transferring the gradient information between meshes (I think that the transfer of potential information is OK  it is only one line!). The boundaries conditions for the noninterface are that T is zero. KM 

June 7, 2006, 13:56 
OK. The mesh stuff was only a

#4 
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Bernhard Gschaider
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OK. The mesh stuff was only a guess. Sorry for asking.
About the BC: it's zero, not zeroGradient? (sorry for asking, but I want to be sure) Does the solution get unbounded in the whole domain or only near your interface? Can you provide us a picture?
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June 8, 2006, 04:40 
are you sure about the code pa

#5 
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Daniele Panara
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are you sure about the code part that compute the normals?
Can you explain better the jump condition? and your BC? In my experience such a problem can appear if you wrong the sign of the heat flux (scalar gradient). Are the heat fluxes pointing in the same direction at the boundary (going in or out from the circle)? Daniele 

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