Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier–Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. First-order error estimates are proved, and stability of a formally second-order variant of the method is established.