摘要
本文分析了Stone引入辅助矩阵(?)将五对角阵A变为七对角阵A+(?)的过程,指出Stone引入的辅助阵(?)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+(?)对称正定。给出选取最优迭代参数①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。
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 matrixA is symmetric and matrix A+ A 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.
出处
《计算物理》
CSCD
北大核心
1989年第4期431-440,共10页
Chinese Journal of Computational Physics
基金
国家自然科学基金
关键词
流体
强隐式格式
收敛性
计算
Computational aerodynamics,SIP scheme,positive definite and symmetric,convergence analysis,numerical calculation.
