ACCURATE DISCRETIZATION OF INCOMPRESSIBLE 3-DIMENSIONAL NAVIER-STOKES EQUATIONS
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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 nature of the solution, the finite analytic method provides an automatic, smooth, gradual upwinding of the three-dimensional convective effect. The finite analytic solutions are then obtained for the lid-driven cavity flow. The results are compared with previous computational results and available experiments. Good agreement is obtained. 1995 Taylor & Francis Group, LLC.