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Diffusion term

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Discretisation of Diffusive Term

  1. Approximation Schemes for diffusive term
  2. Approximation of Diffusive Fluxes
  3. Discretisation on orthogonal grids
  4. 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.
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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