Difference between revisions of "OpenFOAM guide/Owner and neighbour indices"

Latest revision as of 07:49, 3 November 2010

Owner and neighbour indices are a shorthand notation.

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

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

Where:

A_o is the face owner (i.e. the volume cell designated as owner by the mesh);
A_n 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:

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

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:

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

@@ Line 8: / Line 8: @@
 Where:
 * ''A<sub>o</sub>'' is the face ''owner'' (i.e. the volume cell designated as ''owner'' by the mesh);
-* ''A<sub>o</sub>'' is the face ''neighbour'' (i.e. the volume cell designated as ''neighbour'' by the mesh); and
+* ''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.