Calculation on non-orthogonal curvelinear structured grids, finite-volume method
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
Using the finite volume method the trnsformed equations can be integrated as follows:
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