In some past post, I have talked about how we can use artificial compressibility method to solve Navier Stokes equations for steady, incompressible and viscous flow. After completing this task, I am moving on to solve unsteady cases. There is just a slight modification for that. It is not so difficult however not so easy as well.
The method that I am using considers two time steps: pseudo and physical (real). For every real time step, iterations (rather subiterations) are done in pseudo time steps till the local steady solution is achieved. It is better described pictorially in the presentation that I have attached for reference. Because of using C, it is easier for me to use explicit methods because handling matrix in C is difficult. I am still on the go right now as I am waiting for the results.