Cavity flow is simulated using the pressure correction method on a staggered grid using explicit differencing for the hyperbolic terms (CD, MacCormack and Richtmyer method) while both explicit and implicit methods are considered for the diffusive (parabolic) terms. For the implicit steps, preconditioned matrices are used using LU decomposition. The Pressure Poisson equation is also solved implicitly. Neumann boundary conditions are used for pressure and Dirichlet conditions for the velocity field