基于预处理方法的流动数值分析

On Improving Numerical Analysis of Low Speed Flow Using Preconditioning Techniques

以预处理方法为基础 ,采用了有限体积法 ,并将高精度高分辨率迎风格式与隐式时间推进法 LU- SGS格式结合 ,对低速到超音速范围内的流动进行数值分析。为了提高 AUSMPW+ 格式的计算精度 ,采用了三阶 MUSCL格式。为了验证本文方法对低速到超音速范围内的无粘和粘性流动的数值分析效果 ,对几个典型算例进行了数值试验。本文的数值结果与文献计算结果和实验数据基本一致 ,表明本文方法可以有效地对低速到超音速范围内的流动进行数值分析。

A computational method based on preconditioning technique and implicit time marching method was developed. The N-S equations were discretized using finite volume method based on AUSMPW+ (advanced upwind splitting method by pressure based weight functions) to suppress the shortcoming of the existing methods in resolution and precision. The third-order MUSCL (monotone upsteam-centered scheme for conservation laws) scheme proposed by Van leer was used to extend the basic first-order AUSMPW+ formulation to third-order spatial accuracy. The equations were integrated in time using implicit LU-SGS (lower-upper symmetric-Gauss-Seidel) scheme. Computational results for the inviscid flow at M=0.2 and very slow flow with Re=400 are in agreement with test data. It is shown that the method is effective to flow from low speed to supersonic speed with high accuracy and fast convergence.