ACCURATE DISCRETIZATION OF INCOMPRESSIBLE THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS

Abstract

In this article an accurate discretization of three-dimensional incompressible Navier-Stokes equations is derived with the finite analytic method (FAM). The finite analytic method incorporates the local analytic solutions to formulate the discrete algebraic representations of partial differential equations. A very accurate 27-point finite analytic discretization scheme can be derived from local analytic solutions of linearized three-dimensional convection-diffusion equations. Also, a computationally efficient 19-point finite analytic discretization scheme is derived utilizing the superposition of the local analytic solutions of linearized two-dimensional convection-diffusion equations. The accuracy of finite analytic discretization is analyzed. It is shown that using the 27-point scheme as an accurate benchmark case, the 19-paint finite analytic numerical solution is computationally efficient and accurately simulates both convection and diffusion. In this study it is also shown that, due to the analytic n...