计算数学 1980, 2(4) 307-318 DOI:     ISSN: 0254-7791 CN: 11-2125/O1

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流体力学中的差分方法(Ⅱ)——三维涡度方程的数值解

郭本瑜

上海科学技术大学

摘要

有关三维涡度方程的数值计算方面的工作已有[1—3],但缺乏比较系统的理论分析.在[4]中,以二维涡度方程为例,讨论了流体力学差分方法的一些理论问题.本文是把这些结果推广到三维.

关键词

DIFFERENCE METHODS FOR FLUID DYNAMICS (Ⅱ)——NUMERICAL SOLUTION OF THREE--DIMENSIONAL VORTICITY EQUATION

Guo Ben-yu Shanghai University of Science and Technology

Abstract:

In this paper, we generalize the results of [4] to three-dimensional vorticityequations. Two classes of schemes are constructed based on conservation and transport property.The index of generalized stability of schemes for periodic problem is estimated, which showsthe relationship of stability and conservation, solves the convergence of degenerated differenceequation. Two-level schemes are given. Computational errors of such schemes are proved. Theinterference of boundary shape, boundary condition and errors of boundary values are discussedin detail for initial-boundary value problem. Finally the dynamic relaxation method of steadyflow is proposed and its convergence is proved under certain conditions.

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收稿日期  修回日期  网络版发布日期 1980-04-14 00:00:00.0 
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