SIMPLE and staggered grid on boundaries
 

Hi I am fairly a beginner (lacking related coursework) using cfd coding in my research on EHD fows...

I am using SIMPLE with staggered control volumes for U and V ( in the formulation mentioned in the book Numerical Heat Transfer and Fluid Flow by Patankar) with minor embellishments from Peric's codes (I don't have his book)....

(As far as I get from Fig. 6.10 and Article 6.7.3--boundary conditions on pressure correction equation--in the book by Patankar) the grid is usually so designed that :

(a) face of a pressure cv and (b)node for the velocity component normal to boundary

coincides the boundary..this helps to apply the specified normal velocity bc (equivalent to zero gradient of pressure correction)in the pressure correction equation(i.e. continuity)..

Now due to other constraints on some part of boundaries I have the following coinciding with the boundary :

(a) a pressure node (b)face of a cv for velocity-component-normal-to-boundary

I tried half cv as well as one-and-half cv closest to the boundary and applied integral continuity followed by "velocity correction formula" (way of deriving pressure correction equation). I end up involving more than four neighboring points and my solver is for five-point (4 neighbour) computational molecule only. I feel the one-and-half cv still may wrok in an approximate way..

I would appreciate if somebody tells me how or gives clues/ reference to remedy this problem...

You would generally adapt the grid to have pressure nodes on the boundary if you know the pressure value there, so in this case, p' = 0 on the boundary, provided that you start with the value of pressure initialized to the correct (known) value.