Module 6: Solution of Navier-Stokes Equations in Curvilinear Coordinates
  Lecture 38:
 

By analogy to Eqs. (38.1), (38.2) and (38.4), these gradients are calculated as:



(38.13)

The denominator in Eq. (38.13) is equal to the control volume (it represents the vector product of the two vectors and connecting the middle points of opposite of control volume, which is equal to the area enclosed by the CV-faces). Therefore, the source terms for the two momentum equations can be approximated as:



(38.14)

Other source terms can be evaluated in the similar manner.

In some cases cell face fluxes or parts therefore may also be included into the source term. For example, the wall shear stress may be integrated over the CV face and added to S. For example, the U-component:

(38.15)

where is the component of the wall shear stress in the direction of the U-velocity component.

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