AN INCOMPRESSIBLE NAVIER-STOKES MODEL IMPLEMENTED ON NONSTAGGERED GRIDS

Abstract

The present study aims to develop an effective finite-difference model for solving incompressible Navier-Stokes equations. For the sake of programming simplicity, discretization of equations is made on nonstaggered grids without oscillatory solutions arising from the decoupling of the velocity and pressure fields. For the sake of computational efficiency, both segregated and alternating direction implicit (ADI) solution algorithms are employed to reduce the matrix size and, in turn, the CPU time. For the sake of numerical accuracy, a convection-diffusion-reaction finite-difference scheme is employed to provide nodally exact solutions in each ADI solution step. The convective instability problem is thus eliminated, since each convective term is modeled analytically even in multidimensional cases. The validity of the proposed numerical model is rigorously justified by solving one- and two-dimensional problems, which are amenable to analytical solutions. The simulated solutions for the scalar prototype equation agree well with the exact solutions and provide a very high spatial rate of convergence. The same is true for the simulated results of the Navier-Stokes equations.