In this research, a numerical algorithm was developed to solve the incompressible Navier-Stokes equations using explicit time stepping. The goal of this research was to develop an unsteady SIMPLER based algorithm with lower computational overhead. The new explicit algorithm uses a four stage Runge-Kutta scheme to update the velocities and eliminates the need for the pressure correction equation and sub-iterations. This algorithm was derived for use on unstructured tetrahedral grids and was validated with the lid-driven cavity and unsteady rotor flows. This algorithm proved to be easily parallelized and was implemented in CUDA. As a result, accelerations of over 80x are observed compared to a CPU based implicit SIMPLER algorithm using a standard workstation.