Abstract: 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.

Key words: preconditioning method, Navier-Stokes equations, characteristic relations, farfield boundary condition, numerical convergence rate