8.3 – Boundary conditions for the corner volumes

For the boundary conditions described above, it is necessary to use the properties of all fictitious volumes, including the fictitious volumes of the corners, which do not bound the volumes of the physical domain, however their properties enter in the evaluation because the cross terms were in the boundary conditions. Therefore, we need to find an equation for the fictitious volumes of the corners. We do this considering that the properties of the fictitious volumes of the corners are an average of their neighbours, using the following equations:

Northwest corner:



Figure 8.3.1 – Fictitious volume of Northwest corner.
 



(8.3.1)
So
  (8.3.2a)
  (8.3.2b)
  (8.3.2c)
  (8.3.2d)
 
Northeast corner:



Figure 8.3.2 – Fictitious volume of Northeast corner.
 



(8.3.3)
So
 
(8.3.4a)
 

(8.3.4b)
 
(8.3.4c)
 
(8.3.4d)
 
Southeast corner:



Figure 8.3.3 – Fictitious volume of Southeast corner.
 




(8.3.5)
So
 
(8.3.6a)
 

(8.3.6b)
 
(8.3.6c)
 
(8.3.6d)
 
Southwest corner:



Figure 8.3.4 – Fictitious volume of Southwest corner.
 



(8.3.7)
So
 
(8.3.8a)
 

(8.3.8b)
 
(8.3.8c)
 


(8.3.8d)

We should remark that:
  « Energy conservation equation; 
  « Momentum conservation equation in x direction;
  « Momentum conservation equation in y direction.

 
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