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本文的工作主要是借助于现代计算流体动力学（ＣＦＤ）技术的高速发展，讨论应用数值方法来模拟叶轮机械内部的实际流动，以期获取大量真实可靠的流动信息。据此，可以为现代叶轮机械的设计提供一种快速可靠的工具。本文提出了二阶精度隐式矢量单步差分格式并用来求解叶栅的跨音流场，数值试验表明：该方法具有精度高、稳定性好、计算量少、收敛快等优点。
The main work of this paper is based on the rapid development of modern Computational Fluid Dynamics (CFD) technology. The application of numerical methods to simulate the actual flow inside the impeller is discussed in order to obtain a large amount of real and reliable flow information. As a result, a fast and reliable tool for the design of modern impeller machinery can be provided. In this paper, a second-order implicit vector single-step difference scheme is proposed and used to solve the transonic flow fields of cascades. Numerical experiments show that the proposed method has the advantages of high precision, good stability, less computation and fast convergence.