標題: Fourth-order finite difference scheme for the incompressible Navier-Stokes equations in a disk
作者: Lai, MC
應用數學系
Department of Applied Mathematics
關鍵字: Navier-Stokes equations;vorticity-stream function formulation;polar co-ordinates;fast Poisson solver;Runge-Kutta method
公開日期: 20-七月-2003
摘要: 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 (C) 2003 John Wiley Sons, Ltd.
URI: http://dx.doi.org/10.1002/fld.558
http://hdl.handle.net/11536/27706
ISSN: 0271-2091
DOI: 10.1002/fld.558
期刊: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume: 42
Issue: 8
起始頁: 909
結束頁: 922
顯示於類別:期刊論文


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