解不可压缩流体力学问题的降阶法Ⅰ.基本算法

计算物理 ›› 1985, Vol. 2 ›› Issue (3): 337-346.

解不可压缩流体力学问题的降阶法Ⅰ.基本算法

于欣

北京大学数学系

收稿日期:1984-12-22 出版日期:1985-09-25 发布日期:1985-09-25

A DIMENSIONAL REDUCTION METHOD FOR INCOMPRESSIBLE FLUID DYNAMICS I. THE ESSENTIAL ALGORITHM

Yu Xin

Department of Mathematics, Peking University

Received:1984-12-22 Online:1985-09-25 Published:1985-09-25

摘要/Abstract

摘要： 在本系列文章里,我们提出一种新的解不可压缩流体力学问题的有限元方法——降阶法。这种算法是通过寻找空间V~h的一组简单的基函数从而对原来的混合有限元问题降阶来实现的。它的优点是非常节省机时和内存。作为这一系列文章的首篇,本文提出了降阶法的基本算法,并对一个具体的有限元格式给出了空间V~h的非常简单的基函数及降阶法的具体步骤。

Abstract: This paper is the first in a series of papers in which we present a new finite element method for incompressible fluid dynamics——a dimensional reductionmethod.We show that it saves a lot of computing time and storages using this method when a simple basis of Yh is available.in this paper, the essential algorithm is presented, and a very simpte basis of V^h is given for solving the homogeneous Navier-Stokes equations in a simply connected region in R² using quadratic conforming triangular elements for the velocity field and piecewish constant triangular elements for the pressure[1].

于欣. 解不可压缩流体力学问题的降阶法Ⅰ.基本算法[J]. 计算物理, 1985, 2(3): 337-346.

Yu Xin. A DIMENSIONAL REDUCTION METHOD FOR INCOMPRESSIBLE FLUID DYNAMICS I. THE ESSENTIAL ALGORITHM[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1985, 2(3): 337-346.