Development of a continuity-preserving segregated method for incompressible Navier–Stokes equations

The present study aims to develop a new method for obtaining the non-oscillatory incompressible Navier–Stokes solutions on the non-staggered grids. Within the segregated grid framework, the divergence-free equation is chosen to replace one of the momentum equations so as to preserve the fluid incompressibility. For the sake of numerical accuracy, the five-point stencil convection–diffusion–reaction scheme is developed to obtain the nodally exact solution for this chosen momentum equation. The validity of the proposed mass-preserving Navier–Stokes method is justified by solving the three problems which are amenable to analytical solutions. The simulated solution quality is shown to outperform that of the conventional segregated approach, besides gaining a very high spatial rate of convergence.