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Diffusion term

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[[Image:Nm_descretisation_diffusionterms_01.jpg]] <br>
[[Image:Nm_descretisation_diffusionterms_01.jpg]] <br>
'''Figure 1.1''' <br>
'''Figure 1.1''' <br>
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<math> \vec r_{0} </math> and <math> \vec r_{1} </math> are position vector of centroids of cells cell 0 and cell 1 respectively. <br>
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:<math> \vec r_{0} </math> and <math> \vec r_{1} </math> are position vector of centroids of cells cell 0 and cell 1 respectively. <br>
<math> {\rm{d\vec s}} =  \vec r_{1}  - \vec r_{0}  </math>
<math> {\rm{d\vec s}} =  \vec r_{1}  - \vec r_{0}  </math>
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<br>
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===2. Approach 1 ===
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We define vector
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<math>
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\vec \alpha {\rm{ = }}\frac{{{\rm{\vec A}}}}{{{\rm{\vec A}} \bullet {\rm{d\vec s}}}}
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</math>

Revision as of 22:36, 14 September 2005

Discretisation of Diffusive Term

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.
Nm descretisation diffusionterms 01.jpg
Figure 1.1

 \vec r_{0} and  \vec r_{1} are position vector of centroids of cells cell 0 and cell 1 respectively.

 {\rm{d\vec s}} =  \vec r_{1}  - \vec r_{0}


2. Approach 1

We define vector 
\vec \alpha {\rm{ = }}\frac{{{\rm{\vec A}}}}{{{\rm{\vec A}} \bullet {\rm{d\vec s}}}}

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