Finite volume
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All the conservation equations can be written in the same generic differential form: | All the conservation equations can be written in the same generic differential form: | ||
| - | + | <table width="100%"><tr><td> | |
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\frac {\partial( \rho \phi )} {\partial t} + \frac{\partial}{\partial x_{i}} \left( \rho U \phi - \Gamma_{\phi} \frac{\partial\phi}{\partial x_{i}}\right)=S_{\phi} | \frac {\partial( \rho \phi )} {\partial t} + \frac{\partial}{\partial x_{i}} \left( \rho U \phi - \Gamma_{\phi} \frac{\partial\phi}{\partial x_{i}}\right)=S_{\phi} | ||
| - | + | </math> | |
| + | </td><td width="5%">(1)</td></tr></table> | ||
| - | + | Equation (1) is integrated over a control volume and the following discretised equation for <math>\Phi</math> is produced: | |
Revision as of 21:55, 13 September 2005
Discretisation Schemes for convective terms in General Transport Equation. Finite-Volume Formulation, structured grids
Introduction
Here is describing the discretization schemes of the convective terms in the finite-volume equations. The accuracy, numerical stability and the boundness of the solution depends on the numerical scheme used for these terms. The central issue is the specification of an appropriate relationship between the convected variable, stored at the cell centre and its value at each of the cell faces.
Basic Equations of CFD
All the conservation equations can be written in the same generic differential form:
|
| (1) |
Equation (1) is integrated over a control volume and the following discretised equation for 
is produced:
