Dear Sir,

I am solving 2d fluid flow problem using staggered grid (uniform grid with finite difference method), where pressure lies at the grid node and velocities lie at the flux node. We can discretize for the inner node d2p/dx2= (p[i+1]-2p[i]+p[i-1])/delx^2 but Near the boundary we have half control volume. I dont know how to discretize d2p/dx2 using finite difference method. please give some suggestions. thanking you.

If I understand your question, your boundary conditions should take care of the boundary, which will be your (i-1) cell, or your (i+1) cell at the end. You should know values for those.

Use ghost cells which have values copied from the inner region. Refer to general CFD texts with the keyword "ghost cell" or "dummy cell"