Error analysis of a new fractional-step method for the incompressible Navier-Stokes equations with variable density (Q785554)

The paper is concerned with the numerical solution of the incompressible Navier-Stokes equations with variable density. The author extends the operator splitting method proposed for the Navier-Stokes equations with constant density in [\textit{J. Blasco} and \textit{R. Codina}, Appl. Numer. Math. 51, 1--17 (2004; Zbl 1126.76339)]. The proposed scheme is comprised of three steps at every time level. First, an approximate density is obtained as the solution of the density equation using the first-order backward difference scheme. Then, an intermediate velocity is computed as the solution of the linear elliptic equation. Finally, the end-of-step velocity and pressure are computed as the solutions of the generalized Stokes equation. In all steps, the finite element method is used for the spatial discretization. The stability of the proposed method is proved, and temporal error estimates are derived. Numerical experiments are presented to verify theoretical stability results and convergence rates for density, velocity, and pressure.