View source for OpenFOAM guide/Owner and neighbour indices

Owner and neighbour indices are a shorthand notation.

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

<math>\boldsymbol \Psi_f = f \left ( A_o, A_n \right )</math>

Where:
* ''A<sub>o</sub>'' is the face ''owner'' (i.e. the volume cell designated as ''owner'' by the mesh);
* ''A<sub>n</sub>'' is the face ''neighbour'' (i.e. the volume cell designated as ''neighbour'' by the mesh); and
* <math>\boldsymbol \Psi_f</math> is a face field.

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

<math>\mathbf{H}_f \left ( \boldsymbol \psi \right ) = A_n \boldsymbol \psi_n - A_o \boldsymbol \psi_o</math>

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

<math>\sum\limits_o A_{o,i} = \sum\limits_{j=0}^{i-1} A_{ij}</math>

<math>\sum\limits_n A_{n,i} = \sum\limits_{j=i+1}^{N} A_{ji}</math>

Where:
* ''A'' are [[matrix coefficients]]; and
* ''o'' and ''n'' are the [[owner and neighbour indices]].

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

<math>A_{ii} = -\sum\limits_o A_{o,i} -\sum\limits_n A_{n,i}</math>

See also:
* [[Matrices in OpenFOAM]]
[[Category:OpenFOAM coding guide]]