OpenFOAM guide/Owner and neighbour indices

From OpenFOAMWiki

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}

See also: