8.2.1 – Prescribed velocities conditions

Same way to prescribed temperature conditions, the prescribed velocities conditions have, for the fictitious volumes, equations in which the solutions are velocities that are an average between the fictitious volume and the adjacent volume. Therefore these equations are given by:
 
East face:


Momentum conservation in x direction
 



(8.2.1.1)

So
  (8.2.1.2a)
  (8.2.1.2b)
  (8.2.1.2c)
  (8.2.1.2d)

Momentum conservation in y direction
 


(8.2.1.3)

So
 

(8.2.1.4a)
  (8.2.1.4b)
  (8.2.1.4c)
  (8.2.1.4d)
 
West face:


Momentum conservation in x direction
 


(8.2.1.5)

So
 

(8.2.1.6a)
  (8.2.1.6b)
  (8.2.1.6c)
  (8.2.1.6d)

Momentum conservation in y direction
 


(8.2.1.7)

So
  (8.2.1.8a)
  (8.2.1.8b)
  (8.2.1.8c)
  (8.2.1.8d)
 
North face:


Momentum conservation in x direction
 


(8.2.1.9)

So
 

(8.2.1.10a)
  (8.2.1.10b)
  (8.2.1.10c)
  (8.2.1.10d)

Momentum conservation in y direction
 



(8.2.1.11)

So
 


(8.2.1.12a)
  (8.2.1.12b)
  (8.2.1.12c)
  (8.2.1.12d)]
 
South face:


Momentum conservation in x direction
 



(8.2.1.13)

So
 

(8.2.1.14a)
  (8.2.1.14b)
  (8.2.1.14c)
  (8.2.1.14d)

Momentum conservation in y direction
 



(8.2.1.15)

So
 


(8.2.1.16a)
  (8.2.1.16b)
  (8.2.1.16c)
  (8.2.1.16d)
 
 
We should remark that positive signs of and denote the velocities entering at West and South boundaries and leaving from the East and North boundaries of the physical domain. The negative sign occurs when velocity is the opposite direction.
 
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