OpenFOAM guide/Owner and neighbour indices

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Owner and neighbour indices are a shorthand notation.

1 face fields

For equations involving a face field, the owner and neighbour indices are:

$\boldsymbol \Psi_f = f \left ( A_o, A_n \right )$

Where:

• Ao is the face owner (i.e. the volume cell designated as owner by the mesh);
• An is the face neighbour (i.e. the volume cell designated as neighbour by the mesh); and
• $\boldsymbol \Psi_f$ is a face field.

For example, the main equation in lduMatrix;;faceH is:

$\mathbf{H}_f \left ( \boldsymbol \psi \right ) = A_n \boldsymbol \psi_n - A_o \boldsymbol \psi_o$

2 volume fields

For equations involving a volume field, the owner and neighbour indices are given by:

$\sum\limits_o A_{o,i} = \sum\limits_{j=0}^{i-1} A_{ij}$

$\sum\limits_n A_{n,i} = \sum\limits_{j=i+1}^{N} A_{ji}$

Where:

For example, the main equation in lduMatrix;;negSumDiag is:

$A_{ii} = -\sum\limits_o A_{o,i} -\sum\limits_n A_{n,i}$