A STUDY ON NUMERICAL ANALYSIS METHOD OF INCOMPRESSIBLE FLOWS USING HIGH-ORDER ACCURACY FINITE DIFFERENCE METHOD

摘要

The purpose of this study is to establish a finite difference solution in use of high order accurate upwind scheme. Numerical analysis based on a fractional step method has been developed using 3rd-order Adams-Bashforth method for the convective term and Crank-Nicolson method for the viscous term. By computing one-dimensional Burgers-equation and incompressible viscous flow in a three-dimensional cubic cavity, this paper provides a comprehensive accuracy comparison, which shows the advantage of a higher order accurate difference scheme called 3F564. In an analysis of a turbulent channel flow, the solutions at Reynolds number 180, based on the wall shear velocity, and with 64 × 65 × 64 grid points, are in good agreement with existing DNS data. It is made clear that the high order accurate numerical analysis for incompressible flows can be carried out with the method suggested by this study.