iam solving NS equations using FV code and pressure at wall appeared at my equation. What value should i take for P or how do i discretize dp/dy at a cell near the wall? Is backward differencing ok for pressure? Thank you

One usually applies dp/dy = 0 at wall (or dp/dn in general)

This is applied while solving the poisson equation.

Example,

The term d2p/dy2 = (pi+1 - 2pi + pi-1)/dy2 ----(A)

At the lower wall, pi-1 is outside the domain; when you apply dp/dy=0 at lower wall i.e (pi+1 - pi-1)/2dy = 0, OR pi-1 = pi+1

Substitute this back in EQ.(A)

Thus, d2p/dy2 = (2pi+1 - 2pi)/dy2

Strictly speaking, pressure bc is not required for NS equation. Pressure should come out as part of the solution. But in FV method it may be necessary to specify the pressure for evaluating the wall boundary flux. There are several alternatives that can be used:

1. Extrapolate from inside the computational domain.

2. If you want pressure gradient you can use one-sided differences.

3. Setting normal pressure gradient to zero is only an approximation that is valid for thin boundary layers. A more consistent way to do it is to take the projection of the momentum equation along the normal to the wall to get an equation for the normal pressure gradient.