Calculation on non-orthogonal curvelinear structured grids, finite-volume method
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+ | A^{\phi}_{N} = \left( \frac{ \Gamma }{J} \gamma \frac{\Delta \xi}{\Delta \eta} \right)_{n} + max \left[ 0, - \left( \rho V \Delta \xi \right)_{n} \right] | ||
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Revision as of 19:55, 19 August 2010
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
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| (12) |
| (13) |