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Fourth-order finite difference scheme for the incompressible Navier–Stokes equations in a disk

✍ Scribed by Ming-Chih Lai

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
212 KB
Volume
42
Category
Article
ISSN
0271-2091

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✦ Synopsis

Abstract

We develop an efficient fourth‐order finite difference method for solving the incompressible Navier–Stokes equations in the vorticity‐stream function formulation on a disk. We use the fourth‐order Runge–Kutta method for the time integration and treat both the convection and diffusion terms explicitly. Using a uniform grid with shifting a half mesh away from the origin, we avoid placing the grid point directly at the origin; thus, no pole approximation is needed. Besides, on such grid, a fourth‐order fast direct method is used to solve the Poisson equation of the stream function. By Fourier filtering the vorticity in the azimuthal direction at each time stage, we are able to increase the time step to a reasonable size. The numerical results of the accuracy test and the simulation of a vortex dipole colliding with circular wall are presented. Copyright © 2003 John Wiley & Sons, Ltd.

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