一种基于特征关系式的预处理远场边界条件

A farfield boundary condition for preconditioning method based on characteristic relations

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声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Navier-Stokes方程的特征值,原Navier-Stokes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。

Due to large difference between local flow speed and local sound speed,the numerical method originally devised for computation of high-speed compressible flows will suffer from numerical stiff problems to slow down the convergence rate,when the method is extended to computation of low-speed incompressible flows.After the preconditioning matrix is introduced,the original method will be capable of handling low-speed incompressible problems.However,the widely-used farfield boundary condition of Navier-Stokes equations is no longer appropriate for preconditioning systems since the eigenvalues of the equations are altered.Currently,the farfield boundary condition applied to preconditioning equations is much simplified.In this paper,an improved farfield boundary condition is proposed,which is devised based on characteristic relations.The validity of the proposed boundary condition is demonstrated by several typical cases.It is proved that the preconditioning method with appropriate farfield boundary conditions will improve the convergence rate and accuracy of low-speed incompressible flow computations.When the preconditioning method is applied to transonic flow problems,the efficiency and accuracy of the computations reach the same level as the traditional compressible method.The advantages of the proposed farfield boundary condition over the simplified condition lie in two aspects：the convergence rate is accelerated,and the negative effect of insufficient farfield extent is reduced.