Discretisation of Diffusive Term
Note: The approaches those are discussed here are applicable to non-orthoganal meshes as well as orthogonal meshes.
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.
and are position vector of centroids of cells cell 0 and cell 1 respectively.
We wish to approaximate at the face.
Another approach is to use a simple expression for estimating the gradient of scalar normal to the face.
where is suitable face averages.
This approach is not very good when the non-orthogonality of the faces increases. Instead for the fairly non-orthogonal meshes, it is advisable to use the following approaches.
We define vector
giving us the expression:
where and are suitable face averages.
- Ferziger, J.H. and Peric, M. 2002. "Computational Methods for Fluid Dynamics", 3rd rev. ed., Springer-Verlag, Berlin.
- Jasak Hrvoje, PhD. Thesis, "Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows "