Let us consider two-dimensional momentum equation in weak conservative form which is given by
In non-conservative form this may be written as
Here we introduce a term transport-velocity. The transport velocities for the second and third terms on the left hand side are  and  respectively. While dealing with the equations in the conservative form, we shall keep this in mind. For example, during discritization of the term  of Eq. (35.8) we should remember that v is the transport-velocity associated with this term. It is customary to define the transport-velocity at the nodal point where the equation is being defined. In case of the term  we have to refer to Fig. 35.2 and write down the product term  as
Figure 35.2: Definition of the transport velocity at a point where the momentum equation is being discretized.
Finally the discretization of the term  for the  -momentum equation will be accomplished in the following way:
 for 
|
(35.11) |
 for 
|
(35.12) |
Where
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