CFD Online Logo CFD Online URL
Home > Wiki > Diffusion term

Diffusion term

From CFD-Wiki

Revision as of 22:56, 14 September 2005 by Zxaar (Talk | contribs)
Jump to: navigation, search


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}

We wish to approaximate  D_f  = \Gamma _f \nabla \phi _f  \bullet {\rm{\vec A}} at the face.

2. Approach 1

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

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]

where  \bar \nabla \phi _f  and  \Gamma _f   are suitable face averages.

My wiki