I have developed an incompressible viscous flow solver based on an explicit finite difference scheme on a colocated grid. The scheme is first order accurate in time and second order accurate in space.(second order upwinding for convective terms and central for viscous terms). Before advancing the velocity field in time, the pressure field is corrected in order to enforce continuity at the new time level. This is done through the usual pressure poisson eqn formed by taking divergence of the discretised momentum equations.(Computational methods for fluid dynamics-Ferziger & Peric,pp 160-161).The problem that i am facing is that when i am testing the scheme for 2D lid driven cavity problem at Re=1000 and Re=10000 i am getting pressure oscillations in space while the results for the stream function and velocity profiles are in good agreement with reported data. Could you help me locate the problem.

(1). It simply say that, cfd solution to Navier-Stokes equations ,especially for high Reynolds number problems, is still a research field. (2). Even for such seemingly simple 2-D lid driven cavity flow problem, the solution is still hard to come by. (3). Try the existing and working methods first. When you start inventing your method or following methods on a book (just review of methods), you are on your own.

The pressure oscillations with a checker board type spatial pattern are not uncommon in most flow solver, especially in incompressible flows.

The problem comes primarily due to the point-wise decoupling of velocity and pressure, i.e., the velocity update depends on the gradient of pressure and the (Laplacian of) pressure at a point depends on the velocity gradients at that point. So, the velocity at a point is insensitive to the pressure at the point.

The spatial grid can be divided into two different set of alternate grid points like the squares on chess board. The pressure at black points depends only on the velocity at the white points and the velocity at black points depends on the pressure at white points (and vice-versa). Hence, your velocity solution is perhaps smooth even if you have an oscillatory pressure. Standard ways of overcoming this problem are discussed in some detail in this paper.

@article{Zang_94, author = {Zang, Y. and Street, R. L. and Koseff, J. R.}, year = 1994, title = {A non-staggered grid, fractional step method for time dependent incompressible Navier-Stokes equations in curvilinear coordinates}, journal = {Journal of Computational Physics}, volume = 114, number = 1, pages = {18--33}

Good luck.