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November 19, 2010, 07:09 
Gradient at the boundary

#1 
Senior Member

Hi all,
one important thing came to my mind yesterday and I would appreciate your comments on this! Let's say we have a fixedGradient BC, and consider evaluate method for our field: Code:
template<class Type> void fixedGradientFvPatchField<Type>::evaluate(const Pstream::commsTypes) { if (!this>updated()) { this>updateCoeffs(); } Field<Type>::operator= ( this>patchInternalField() + gradient_/this>patch().deltaCoeffs() ); fvPatchField<Type>::evaluate(); } fi(wall) = fi(cell_center) + Grad0 * d Is this a really correct estimation??? For example, if we use fourth order inside the domain for the interpolation and we end up with only (2nd?) order at the boundary using such BC type? I would really appreciate your comments! Have a nice day! Alexander
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Advanced Process Simulation of Solidification and Melting" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben FranzJosefStr. 18 A  8700 Leoben Österreich / Austria Tel.: +43 3842  402  3125 http://smmp.unileoben.ac.at Last edited by makaveli_lcf; November 19, 2010 at 09:18. 

November 19, 2010, 10:01 

#2 
Senior Member
Francois
Join Date: Jun 2010
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Dear Alexander,
The lower order estimation on the boundary is correct. Of course you would also like a higherorder estimation on the boundary, but because it makes the implementation of such a scheme more complex, a lower order estimation on the boundary is acceptable. It should not influence the order of convergence of the solution in your domain. So your overall solution will not degrade from forth order accurate to second order accurate because you only use a second order accurate gradient estimation scheme on the boundary. I hope this helps! Kind regards, Francois. 

November 19, 2010, 10:08 

#3 
Senior Member

Francois, thank you for your reply!
Another point to discuss: there is no nonorthogonal correction at the boundary: Code:
00161 // Return gradient at boundary 00162 virtual tmp<Field<Type> > snGrad() const 00163 { 00164 return gradient_; 00165 }
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Advanced Process Simulation of Solidification and Melting" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben FranzJosefStr. 18 A  8700 Leoben Österreich / Austria Tel.: +43 3842  402  3125 http://smmp.unileoben.ac.at 

November 21, 2010, 13:59 

#4 
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Francois
Join Date: Jun 2010
Posts: 107
Rep Power: 7 
Dear Alexander,
Could you not try a dot product between the velocity component and the the face area? Something like: Code:
boundaryUxValue = ( Ux & yourBoundaryPatch.patch().Sf() ); etc. François. 

November 21, 2010, 16:47 

#5 
Senior Member

François, what should I check with this? Do you mean dot product between total velocity and normal vector to estimate flux?
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Advanced Process Simulation of Solidification and Melting" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben FranzJosefStr. 18 A  8700 Leoben Österreich / Austria Tel.: +43 3842  402  3125 http://smmp.unileoben.ac.at 

November 22, 2010, 08:57 

#6 
Senior Member
Francois
Join Date: Jun 2010
Posts: 107
Rep Power: 7 
Dear Alexander,
Yes. If you are afraid that the inbuilt implementations do not compute/use the solutions you expect, you can easily check that the values OpenFOAM uses are similar to those you would use in your own implementation. I thought this might help for your boundary. Kind regards, Francois. 

November 22, 2010, 12:20 

#7  
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Francois
Join Date: Jun 2010
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Hum. A quick look at the wiki also returned the following answer. This should take care of the issues altogether.
Quote:
Kind regards, Francois. 

December 27, 2010, 05:53 
Correction at boundary

#8 
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Andrea Petronio
Join Date: Mar 2009
Location: Trieste, Italy
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Hi all,
can anyone clarify me this point, please: chosen a corrected scheme for the Laplacian computation, the nonorthogonal correction is applied automatically to the boundaries too? Thank you Andrea 

December 30, 2010, 12:05 
Correction at boundary

#9 
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Andrea Petronio
Join Date: Mar 2009
Location: Trieste, Italy
Posts: 38
Rep Power: 8 
Hi all,
I'm confused about 2 points: looking into http://foam.sourceforge.net/doc/Doxy...8C_source.html I see on line 309: Code:
// Boundary correction vectors set to zero for boundary patches // and calculated consistently with internal corrections for // coupled patches seems to be not implemented. And I read from many source that DeltaCoeffs() should be simply the inverse of the cell center to cell center vector while in the code is replaced by Code:
// Stabilised form for bad meshes DeltaCoeffs[facei] = 1.0/max(unitArea & delta, 0.05*mag(delta)); Comments on these are appreciate Andrea 

January 13, 2012, 13:48 

#10 
Senior Member
Philip Cardiff
Join Date: Mar 2009
Location: Dublin,Ireland
Posts: 577
Rep Power: 19 
Hi,
I have been looking at the calculation of gradients (fvc::grad) and surfacenormal gradients (fvc::snGrad, and fvc::laplacian). As far as I can see, the snGrad is calculated incorrectly on nonorthogonal fixedValue boundaries. There should be nonorthogonal correction on fixedValue boundaries but it is set to zero (in surfaceInterpolation.C). I have prepared a simple utility to check: Code:
\**/ #include "fvCFD.H" #include "fixedGradientFvPatchFields.H" int main(int argc, char** argv) { # include "setRootCase.H" # include "createTime.H" # include "createMesh.H" Info << "Testing field operations" << nl << endl; //// // define rotation //// scalar theta = 1; // degrees const scalar PI = 3.141592; theta *= PI; theta /= 180; tensor rotMat(::cos(theta), (::sin(theta)), 0, ::sin(theta), ::cos(theta), 0, 0, 0, 1); //// //// Info << "Reading alpha" << endl; volVectorField alpha ( IOobject ( "alpha", runTime.timeName(), mesh, IOobject::MUST_READ, IOobject::NO_WRITE ), mesh // ((rotMat & mesh.C())  mesh.C()), //fixedValueCorrectedFvPatchVectorField::typeName //fixedValueFvPatchVectorField::typeName //fixedGradientCorrectedFvPatchVectorField::typeName //fixedGradientFvPatchVectorField::typeName //boundaryTypes ); //// //// Info << nl << "Setting alpha field" << endl; //// // increment time runTime++; // set the internal field alpha = ((rotMat & mesh.C())  mesh.C()); // set the fixedValue and fixedGradient boundaries forAll(alpha.boundaryField(), patchi) { if(alpha.boundaryField()[patchi].type() == fixedValueFvPatchVectorField::typeName) { Info << "\tSetting alpha fixedValue boundaries for patch " << mesh.boundary()[patchi].name() << endl; const vectorField& patchC = mesh.boundaryMesh()[patchi].faceCentres(); alpha.boundaryField()[patchi] == ((rotMat & patchC)  patchC); } else if(alpha.boundaryField()[patchi].type() == fixedGradientFvPatchVectorField::typeName) { Info << "\tSetting alpha fixedGradient boundaries for patch " << mesh.boundary()[patchi].name() << endl; vectorField n = mesh.boundary()[patchi].Sf() / mesh.boundary()[patchi].magSf(); fixedGradientFvPatchVectorField& alphaPatchGrad = refCast<fixedGradientFvPatchVectorField>(alpha.boundaryField()[patchi]); // analytical internal gradAlpha is (rotMat.T()  I) // therefore analytical boundary gradient is: alphaPatchGrad.gradient() = n & (rotMat.T()  I); } else { FatalError << "The geometry should only have boundaries of type" << " fixedValue or fixedGradient!" << exit(FatalError); } } alpha.write(); //// surfaceVectorField n = mesh.Sf()/mesh.magSf(); //// // gradient of vector field // least squares seems right in the boundary cells... // Gauss linear is wrong in all skewed cells as expected //// Info << nl << "Writing out the gradient" << endl; volTensorField gradAlpha ( IOobject ( "gradAlpha", runTime.timeName(), mesh, IOobject::NO_READ, IOobject::NO_WRITE ), fvc::grad(alpha) ); Info << "\tMax mag is " << max(mag(gradAlpha)).value() << "\tMin mag is " << min(mag(gradAlpha)).value() << endl; gradAlpha.write(); //// //// // laplacian of alpha // lapAlpha is fine when the BC of alpha are fixedValue but lapAlpha is // wrong in the boundary cells when the BC is fixedGradient... assuming I // set the fixedGradient BCs correctly //// Info << nl << "Writing out the laplacian of alpha" << endl; volVectorField lapAlpha ( IOobject ( "lap(alpha)", runTime.timeName(), mesh, IOobject::NO_READ, IOobject::NO_WRITE ), fvc::laplacian(alpha, "lap(alpha)") // equivalent to fvc::surfaceIntegrate(fvc::snGrad(alpha)*mesh.magSf()) ); Info << "\tMax mag is " << max(mag(lapAlpha)).value() << "\tMin mag is " << min(mag(lapAlpha)).value() << endl; lapAlpha.write(); //// Info << nl << endl; return 0; } grad(alpha) should have the constant components (0.00015, 0.017452, 0, 0.017452, 0.00015, 0, 0, 0, 0) and laplacian(alpha) should be (0, 0, 0).The alpha field actually corresponds to rigid rotation about the zaxis. fvc::grad(alpha) is calculated and seems correct, but the fvc::laplacian(alpha) is incorrect on nonorthogonal fixedValue boundaries! I have attached a nonorthogonal test case which shows the problem. Does anybody have any thoughts on this, am I misunderstanding something? Philip Edit: by the way, fvc::laplacian(alpha) is correct for fixedGradient boundaries because they don't need nonorthogonal correction as the surfacenormal gradient is already known. Edit2: I tried this on OpenFOAM2.1.x and OpenFOAM1.6ext with the same results. Also I checked old foam code and it seems to have no correction on the boundaries too, hmnnn... 

November 25, 2012, 16:26 

#11 
Senior Member
Philip Cardiff
Join Date: Mar 2009
Location: Dublin,Ireland
Posts: 577
Rep Power: 19 
Hi,
for future reference, OpenFOAM sets nonorthogonal correction to zero on the boundaries. As described in Hrv's thesis, it is assumed that the dependent variable is uniform along the boundary face and hence no nonorthogonal correction is applied. However, there are cases (for instance in solid mechanics) when this is a poor assumption and it is assumed that the dependent variable varies linearly along the boundary face and boundary nonorthogonal corrections are imperative. So if you need boundary nonorthogonal correction then custom boundary conditions must be used where nonorthogonal corrections are imposed (see here). Philip 

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