I want to solve Navier Stokes equations on a collocated grid. Earlier, I was using a MacCormick scheme based solver where I discretized predictor step in forward differences and corrector step in backward differences as mentioned in this paper (An explicit finite-difference scheme for simulation of moving particles, http://dl.acm.org/citation.cfm?id=1127013). This works, but the convergence is very slow at high-grid resolutions.
In this regard, can anyone suggest me some explicit NS solvers that are not very complicated and could be converged in relatively shorter times. Also, it should be mentioned here that I am writing NS equations in artificial compressibility framework.