计算流体中一个改进的强隐式格式及迭代的收敛性

计算物理 ›› 1989, Vol. 6 ›› Issue (4): 431-440.

计算流体中一个改进的强隐式格式及迭代的收敛性

王保国, 陈乃兴

中国科学院工程热物理所, 北京

收稿日期:1987-09-08 出版日期:1989-12-25 发布日期:1989-12-25
基金资助:
国家自然科学基金

AN IMPROVED SIP SCHEME AND CONVERGENCE ANALYSIS OF THE ITERATIVE PROCEDURE IN FLUID MECHANICS

Wang Baoguo, Chen Naixing

Institute of Engineeirng Thermophysics Chinese Academy of Sciences, Beijing

Received:1987-09-08 Online:1989-12-25 Published:1989-12-25

摘要/Abstract

摘要： 本文分析了Stone引入辅助矩阵Ã将五对角阵A变为七对角阵A+Ã的过程,指出Stone引入的辅助阵Ã不具备对称性,由此会给迭代收敛的分析工作带来困难。在此分析的基础上构造了一个对称的辅助矩阵,当A为对称时可使A+Ã对称正定。给出选取最优迭代参数ω的公式和办法。通过典型算例对这种改进的强隐式格式的数值稳定性作了验证。

关键词: 强隐式格式, 对称正定阵, 习文敛性分析, 跨音速流动

Abstract: A new improved Strongly Implicit Procedure is presented for solving the large sets of equations with matrix of coefficients A in fluid mechanics.This algorithm has several advantages over those now in use.First,auxiliary matrix Ã is symmetric and matrix A+Ã is positive definite and symmetric matrix when A is symmetric.This ensures the numerical stability of the iterative algorithms.Second,for an appropriate choice of iterative parameter ω,the rate of convergence of the new iterative procedure should be faster than original SIP scheme.Numerical results of two dimensional flows are given with the scheme. It is shown that the algorithm is very efficient.

Key words: Computational aerodynamics, SIP scheme, positive definite and symmetric, convergence analysis, numerical calculation

王保国, 陈乃兴. 计算流体中一个改进的强隐式格式及迭代的收敛性[J]. 计算物理, 1989, 6(4): 431-440.

Wang Baoguo, Chen Naixing. AN IMPROVED SIP SCHEME AND CONVERGENCE ANALYSIS OF THE ITERATIVE PROCEDURE IN FLUID MECHANICS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 6(4): 431-440.