IMPROVEMENT OF FINITE-ANALYTIC DISCRETIZATION OF INCOMPRESSIBLE 3-DIMENSIONAL NAVIER-STOKES EQUATIONS

The finite-analytic numerical method is presented for discretization of three-dimensional incompressible Navier-Stokes equations. In this article, a new 27-point finite-analytic discretization scheme is derived utilizing the superposition of the local analytic solutions of linearized hue-dimensional convection-diffusion equation. It is shown that the new 27-point finite-analytic numerical solution is computationally efficient and accurately simulates both convection and diffusion, due to the analytic nature of the solution, which provides an automatic, smooth, gradual upwinding of the three-dimensional convective effect.