摘要
提出一种求解时间相关、三维不可压完全Navier-Stokes方程的影响矩阵法。考虑流动区域为上半空间的平极边界层流动,在水平方向,利用周期性条件,采用Fourier离散,在半无穷方向,定义了一种特殊映像并利用Chebyshev多项式展开。由此将Navier-Stokes方程转化为以水平波数(k1,k2)为参数的一组法向Helmholtz方程组,同时可更有效地求解压力。本文讨论了连续问题的影响矩阵法与原问题的等价性。影响矩阵法的离散形式,以及影响矩阵法的算法实现等。最后给出了一维Helmholty问题的数值实验结果。
This paper presents an influent matrix method (IMM) of solving three dimensional, unsteady and incompressible full Navier Stokes equations. Boundary layer transition problem in upper half space is studied. By means of periodic conditions in the horizontal directions, Fourier spectral discretization is used. One special transform is defined and the unknown function is expanded on Chebyshev polynomials in the normal direction. The most obvious one of advantages for IMM is that the Navier Stokes equations can be changed into one set of the Helmholtz equations with the pair of parameters of (k 1, k 2), the horizontal wavenumbers. The equivalence of the continuous problem and the IMM equations, the discrete form of the IMM equations, and the code performance of the IMM are discussed. Numerical experiments are fulfilled on one dimensional Helmholtz problem.
出处
《航空计算技术》
1999年第1期1-5,共5页
Aeronautical Computing Technique
基金
国防科工委96预研基金
国家教育部96优秀青年教师基金
西安交通大学科研基金
关键词
影响矩阵法
边界层流动
直接数值模拟
转换
Influent matrix method Boundary layer transition Direct numerical simulation Navier Stokes equations Helmholtz equations