A numerical flow simulation based on the rate form of the equation of state

A finite-difference numerical method of solution for the unsteady, incompressible Navier-Stokes equations using primitive variables is presented. The rate form of the equation of state is used for the calculation of pressure. This form of the equation of state is well-suited for use with the unsteady form of the conservation equations (mass, momentum and energy). An implicit algorithm is used for the time integration for greater numerical stability. This method is used to solve a known benchmark problem in steady-state natural convection as a test of steady-state accuracy. The results of the simulation are compared to the benchmark.