A divergence-free-condition compensated method for incompressible Navier–Stokes equations

The present study aims to develop a new formulation to effectively calculate the incompressible Navier–Stokes solutions in non-staggered grids. The distinguished feature of the proposed method, which avoids directly solving the divergence-free equation, is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility. For the sake of numerical accuracy, dispersion-relation-preserving upwind scheme developed within the two-dimensional context was employed to approximate the convection terms. The validity of the proposed mass-preserving Navier–Stokes method is justified by solving two benchmark problems at high Reynolds and Rayleigh numbers. Based on the simulated Navier–Stokes solutions, the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of CPU time.