Jacobian系数矩阵分裂法与气动方程的数值计算

前言 七十年代中期,人们多采用显式方法数值求解可压缩的Navier-Stokes方程.这种方法简单易解,但由于稳定性对时间步长的限制,使得求解所需机时颇多.在求解定常问题时,数值求解过程可以与真实的物理发展过程不对应,人们可以根据需要而改变求解过程,以达到加速收敛的目的.Allen和Cheng就是根据这种思想计算了近底部分离流动.为了达到加速得到定常解的目的,很多人采用在不同空间点上取变时间步长的方法.在[5]中,当调节因子取标量形式时,相当于取变时间步长的方法.如果调节因子或算子放大修正系数取矩阵形式,则可得到更快的收敛速度.Beam和Warming在[7]中提出了一个非迭代的隐式方法,并在空间坐标方向上利用近似因式分解,大大提高了隐式格式的使用效率.Steger和Warming在[8]中详细介绍了流通量分裂法.1985年,MacCormack在[9]中改进了自己在[10]中提出的二步隐式方法.作者在[11]中也用流

JACOBIAN MATRIX SPLITTING METHODS AND NUMERICAL COMPUTATION OF AERODYNAMICS EQUATIONS

The flux vector splitting technique is widely used in solving aerodynamics equations. Inthe present paper different Jacobian matrix splitting methods are considered. By Taylor ex-pansion series, different differnce schemes are obtained which are linear and requires nospecial linearization, Then, Simple and efficient implicit difference schemes are obtained withspecially chosen matrix splitting. Practical applications show that the suggested method is ef-ficient.