Calculation on non-orthogonal curvelinear structured grids, finite-volume method
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:<math> | :<math> | ||
\frac{\partial}{\partial \xi} \left( \rho U \phi \right) + \frac{\partial }{ \partial \eta } \left( \rho V \phi \right) = \frac{\partial}{\partial \xi} \left[ \frac{\Gamma }{J} \left( \alpha \frac{\partial \phi}{\partial \xi} - \beta \frac{\partial \phi}{ \partial \eta} \right) \right] + \frac{\partial}{\partial \eta} \left[ \frac{\Gamma}{J} \left( \gamma \frac{\partial \phi}{\partial \eta} - \beta \frac{\partial \phi}{ \partial \xi} \right) \right] + J S^{\phi} | \frac{\partial}{\partial \xi} \left( \rho U \phi \right) + \frac{\partial }{ \partial \eta } \left( \rho V \phi \right) = \frac{\partial}{\partial \xi} \left[ \frac{\Gamma }{J} \left( \alpha \frac{\partial \phi}{\partial \xi} - \beta \frac{\partial \phi}{ \partial \eta} \right) \right] + \frac{\partial}{\partial \eta} \left[ \frac{\Gamma}{J} \left( \gamma \frac{\partial \phi}{\partial \eta} - \beta \frac{\partial \phi}{ \partial \xi} \right) \right] + J S^{\phi} | ||
+ | </math> | ||
+ | </td><td width="5%">(2)</td></tr></table> | ||
+ | |||
+ | where | ||
+ | |||
+ | <table width="70%"><tr><td> | ||
+ | :<math> | ||
+ | U = \overline{u} \frac{\partial y}{\partial \eta} - \overline{v} \frac{\partial x}{\partial | ||
</math> | </math> | ||
</td><td width="5%">(2)</td></tr></table> | </td><td width="5%">(2)</td></tr></table> |
Revision as of 16:23, 17 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
| (2) |