Difference between revisions of "OpenFOAM guide/Discretization coefficients"
From OpenFOAMWiki
(Created page with 'Discretization coefficients are coefficients that result from the discretization of the problem. They are closely related to the matrix coefficients. OpenFOAM uses …') |
Makaveli lcf (Talk | contribs) |
||
(One intermediate revision by one other user not shown) | |||
Line 13: | Line 13: | ||
* '''S''' is the source term. | * '''S''' is the source term. | ||
− | The neighbour cells, indexed by '' | + | The neighbour cells, indexed by ''r'', depend on the size of the computational molecule, which depends on the [[discretization]] scheme. For simple [[discretization]] schemes, the neighbour cells only includes adjacent cells; whereas for higher order schemes, more distant cells are included in the summation. In orthogonal grids, the notation for the neighbours is usually expressed in terms of compass directions; however this cannot be used in unstructured grids. |
See also: | See also: |
Latest revision as of 10:42, 16 April 2011
Discretization coefficients are coefficients that result from the discretization of the problem. They are closely related to the matrix coefficients. OpenFOAM uses matrix coefficients in its source code.
The discretization coefficients have the form:
Where:
- p is the cell volume for which the equation applies;
- r are the related cell volumes (i.e. in close proximity to cell p)[1];
- A are the discretization coefficients;
- is the variable being solved for; and
- S is the source term.
The neighbour cells, indexed by r, depend on the size of the computational molecule, which depends on the discretization scheme. For simple discretization schemes, the neighbour cells only includes adjacent cells; whereas for higher order schemes, more distant cells are included in the summation. In orthogonal grids, the notation for the neighbours is usually expressed in terms of compass directions; however this cannot be used in unstructured grids.
See also: