From CFD-Wiki
2D case
For calculations in complex geometries boundary-fitted non-orthogonal curvlinear grids is usually used.
General transport equation is transformed from the physical domain into the computational domain as the following equation
-
| (2) |
where
-
| (3) |
-
| (4) |
-
| (5) |
-
| (6) |
-
| (7) |
-
| (8) |
Using the finite volume method the trnsformed equations can be integrated as follows:
-
| (9) |
The convection terms are approximated as described in section http://www.cfd-online.com/Wiki/Discretization_of_the_convection_term .
Diffusion terms are approximated by the second-oder central differencing scheme.
The standard form of the finite volume equation can be obtained as
-
| (10) |
where
-
| (11) |
-
| (12) |
-
| (13) |
-
| (14) |
-
| (15) |