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高速可压缩流动的计算方法应用于不可压低速问题会因为当地速度和当地音速量级相差较大产生刚性问题并导致数值收敛困难。预处理方法引入预处理矩阵使传统的可压缩方法具备了求解不可压或低速问题的能力。由于预处理方程改变了N-S方程的特征值,原N-S方程的远场边界条件不再适用。目前被广泛使用的预处理方程的远场边界条件为简化边界条件。本文以预处理方程为基础进行分析,推导了一种基于特征关系式的远场边界条件。通过典型状态算例数值实验,验证了该边界条件及预处理方法的有效性。结果显示,对于定常/非定常低速不可压流动,合理地设置远场边界条件,预处理方法都能够提高计算的收敛性和精度;对于跨声速流动,预处理方法和未加预处理方法两者的计算效率和计算精度相当。本文的预处理远场边界条件与简化预处理远场边界条件相比一是能够进一步提高计算的收敛速度;二是能够有效降低远场边界位置对预处理方法数值计算结果的负面影响。
The calculation method of high speed compressible flow applied to non-compressible low-speed problems will produce rigid problems due to large difference between local speed and local sound speed and lead to numerical convergence difficulties. The introduction of pretreatment methods into the preprocessing matrix enables the traditional compressibility method to solve the problem of incompressible or low speed. Since the pretreatment equation changes the eigenvalue of the N-S equation, the far-field boundary conditions of the original N-S equation are no longer applicable. The far-field boundary conditions of the widely used pretreatment equations simplify the boundary conditions. Based on the pretreatment equation, this paper derives a far-field boundary condition based on the characteristic relation. Through numerical experiments of a typical state example, the validity of the boundary conditions and the pretreatment method is verified. The results show that both the preconditioning method and the preconditioning method can improve the convergence and precision of the computations for the steady-state / unsteady low-pressure incompressible flows and the far-field boundary conditions are set reasonably. For both transonic flows, both pretreatment and non-pretreatment methods The calculation efficiency and calculation accuracy are quite. The preconditioned far-field boundary conditions in this paper are compared with the simplified preconditioned far-field boundary conditions to further improve the convergence rate of the calculation. Second, the negative influence of the far-field boundary position on the numerical results of the pretreatment method can be effectively reduced.