Diffusion term

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

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.

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 $\vec \alpha {\rm{ = }}\frac{{{\rm{\vec A}}}}{{{\rm{\vec A}} \bullet {\rm{d\vec s}}}}$