轴对称跨声速流全速势方程的一种解法

An Approximate Factorization Method Solving Axisym-metric Transonic FulI PotentiaI Equation

本文将Ｈｏｌｓｔ的求解跨声速全速势方程的ＡＦ２格式，推广到求解相应的轴对称流动问题，基本思想是将轴对称流的速度势方程分解为二维流效应和轴对称流效应两部分。在计算残值时，自然以上两邻分都要考虑，但在进行近似子分解时，只考虑二维流部分，而略去轴对称效应部分。算例表明，本方法收敛性很好，一般只要迭代３０至５０次。物体被考虑为半无限长的旋转体，而对有限长的物体则可看作截面积收缩为零的特例。采用Ｃ型网格的贴体坐标。用ＬａＪａｃｅ方程生成网格，并用快速收敛的ＡＦ１格式求解。

The well-known Holst scheme solving the transonic full potential equation is extended to the axisvmmetric case in the present paper.The disadvantages of the axial governing equation are as follows.The governing equation is singular on the symmetric axis and near the far Iield. Moreoyer, the coefficients of the governing equation vary seriously due to the appearance of radial coordinate in the equation, while the stability analysis of approximate schemes is based on equations of constant coefficients.In the present paper, the governing equation is divided by the radial coordinate,and the above disadvantages are eliminated. In such doing, the governing equation consists of two parts,i.e. the two-dimensional part, and that for axial flow correction. In the present paper, only the two-dimensional part of the governing equation is con-sidered in the approximate factorization scheme, while the full equation has to be used in the computation of residual in order to obtain correct flow solution. Numerical experiment shows that the present technique possesses fairly good convergence property of about 30～50 iterations for the flow field computation.