Calculation on non-orthogonal curvelinear structured grids, finite-volume method
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+ | b^{\phi} = \left( J \Delta \xi \Delta \eta \right) \overline{S}^{\phi}_{P} - \left[ \frac{\Gamma \Delta \eta}{J} \left( \beta \frac{\partial \phi}{\partial \eta} \right) \right]^{e}_{w} - \left[ \frac{\Gamma \Delta \xi}{J} \left( \beta \frac{\partial \phi}{\partial \xi} \right) \right]^{n}_{s} | ||
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+ | </td><td width="5%">(15)</td></tr></table> |
Latest revision as of 10:24, 20 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
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where
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