Diffusion term
From CFD-Wiki
Contents |
Discretisation of Diffusive Term
Sub-topics
- Approximation Schemes for diffusive term
- Approximation of Diffusive Fluxes
- Discretisation on orthogonal grids
- Discretisation on non-orthogonal curvilinear body-fitted grids
1. Description
A control volume in mesh is made up of set of faces enclosing it. The figure 1.1 shows a typical situation. Where A represent the magnitude of area of the face. And n represents the normal unit vector of the face under consideration.
Figure 1.1
and 
are position vector of centroids of cells cell 0 and cell 1 respectively.
We wish to approaximate 
at the face.
2. Approach 1
We define vector
giving us the expression:
![D_f = \Gamma _f \nabla \phi _f \bullet {\rm{\vec A = }}\Gamma _{\rm{f}} \left[ {\left( {\phi _1 - \phi _0 } \right)\vec \alpha \bullet {\rm{\vec A + }}\bar \nabla \phi \bullet {\rm{\vec A - }}\left( {\bar \nabla \phi \bullet {\rm{d\vec s}}} \right)\vec \alpha \bullet {\rm{\vec A}}} \right]](/W/images/math/7/7/2/772b96059e9032fc07b25c0dee76db6c.png)
where 
and 
are suitable face averages.
