implicit div(kgrad(au))

gunnar2 · August 8, 2011, 13:45

Hello,
I have asked in "Running / Solving / CFD (http://www.cfd-online.com/Forums/ope...-k-grad-u.html)" before, but now this seems to be a programming question.

How can I treat $\nabla\cdot k \nabla \alpha u$ implicitly?

- scalar field (known diffusivity)
$\alpha$ - scalar field (known mass fraction)

- scalar field (unknown)

fvm::laplacian(k,alpha*u) generates a compiler error.

I think a possible solution is to right-multiply the fvMatrix fvm::laplacian(k,u) with a diagonal matrix $D_\alpha$ made up of the values of $\alpha$ on it's diagonal.

But how do I write this in C++?

Thank you
Gunnar

gunnar2 · August 9, 2011, 14:22

Is it really not possible to build a diagonal matrix?

Another possibility can be first to construct

fvMatrix M=fvm::laplacian(k,u)

In the next step I would have to multiply each row i of the matrix M with alpha[i]. However I don't understand the storage format of fvMatrix. May I ask if somebody would share a few lines of code, how to multiply one row of a fvMatrix with a scalar value?

Thank you
Gunnar

gunnar2 · August 11, 2011, 16:40

anybody any idea?

or at least a reason, why there cannot be an implicit scheme for $\nabla\cdot k\nabla\alpha u?$

Thank you
Gunnar

marupio · August 12, 2011, 08:52

Can you use the chain rule to seperate alpha and u?

jakobh · August 12, 2011, 11:41

Hi Gunnar!
You can use this function:

Code:

namespace Foam{ namespace fvm{
  template<class Type, class GType>
  tmp<fvMatrix<Type> >
  laplacian
  (
    const GeometricField<GType, fvPatchField, volMesh>& gamma,
    GeometricField<Type, fvPatchField, volMesh>& vf,
    GeometricField<Type, fvPatchField, volMesh>& alpha
  )
  {
    tmp<fvMatrix<Type> > Laplacian=fvm::laplacian(gamma,vf);
    Laplacian()*=alpha;
    return Laplacian;
  }
} }

In your case: fvm::laplacian(k,u,alpha)

Jakob

ziemowitzima · August 21, 2011, 14:57

Hi Jakob,
I read your post and it seems that you can know the answer for my question with laplacian operator.
If you dont mind please read my post at:
http://www.cfd-online.com/Forums/ope...n-problem.html

August 8, 2011, 13:45	*implicit div(kgrad(au))*	#1
gunnar2 New Member Join Date: Aug 2011 Posts: 6 Rep Power: 14	Hello, I have asked in "Running / Solving / CFD (http://www.cfd-online.com/Forums/ope...-k-grad-u.html)" before, but now this seems to be a programming question. How can I treat $\nabla\cdot k \nabla \alpha u$ implicitly? - scalar field (known diffusivity) $\alpha$ - scalar field (known mass fraction) - scalar field (unknown) fvm::laplacian(k,alpha*u) generates a compiler error. I think a possible solution is to right-multiply the fvMatrix fvm::laplacian(k,u) with a diagonal matrix $D_\alpha$ made up of the values of $\alpha$ on it's diagonal. But how do I write this in C++? Thank you Gunnar

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August 9, 2011, 14:22		#2
gunnar2 New Member Join Date: Aug 2011 Posts: 6 Rep Power: 14	Is it really not possible to build a diagonal matrix? Another possibility can be first to construct fvMatrix M=fvm::laplacian(k,u) In the next step I would have to multiply each row i of the matrix M with alpha[i]. However I don't understand the storage format of fvMatrix. May I ask if somebody would share a few lines of code, how to multiply one row of a fvMatrix with a scalar value? Thank you Gunnar

August 11, 2011, 16:40		#3
gunnar2 New Member Join Date: Aug 2011 Posts: 6 Rep Power: 14	anybody any idea? or at least a reason, why there cannot be an implicit scheme for $\nabla\cdot k\nabla\alpha u?$ Thank you Gunnar

August 12, 2011, 08:52		#4
marupio Senior Member David Gaden Join Date: Apr 2009 Location: Winnipeg, Canada Posts: 437 Rep Power: 22	Can you use the chain rule to seperate alpha and u?

August 21, 2011, 14:57		#6
ziemowitzima Senior Member Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 145 Rep Power: 17	Hi Jakob, I read your post and it seems that you can know the answer for my question with laplacian operator. If you dont mind please read my post at: http://www.cfd-online.com/Forums/ope...n-problem.html

implicit div(k*grad(a*u))

implicit div(kgrad(au))