目前针对流体机械流动问题的数值模拟方法大都是基于欧拉描述法基础上的，而三维涡方法作为一种拉格朗日型的数值模拟方法，其在计算中的优点逐渐引起人们的重视。三维涡方法无需划分体网格，在计算中不会引入数值粘性；涡方法还是一种自适应方法，计算区域主要集中在涡量存在的地方，从而可以提高计算效率和精度；对于不可压缩流动，涡量输运方程不包含压力项，此时可以分别求解涡量输运方程和压力Poisson方程；此外，从理论上来讲，三维涡方法易于进行并行计算，可以高效地解决大尺度流场的计算问题。在已有三维涡方法的基础上，本文提出了一种新型的混合三维涡方法。该方法将计算流场分为势流场和涡量场。在计算涡量场时，采用涡团模型进行离散，通过拉格朗日型涡量输运方程，采用Chorin提出的分步法来追踪离散涡元的扩散和强度的变化，从而描述整个涡量场。在计算势流场时，为保持涡方法的无网格特性，采用边界元法计算势流场以满足边界的不可穿透条件，通过在边界上引入新生涡以满足边界的无滑移条件。在本文提出的混合三维涡方法计算流场的过程中：首先，在拉格朗日框架下计算离散涡元的迁移速度；通过广义毕奥-萨伐尔公式计算离散涡元的诱导速度；粘性扩散项在数值边界层内采用随机走步法处理，在计算流域则采用粒子强度交换法处理；采用快速多极子算法处理涡元诱导速度和边界元法中满秩矩阵的计算量和存储量大的问题；采用正则化算法来处理边界元法中遇到的强奇异积分问题；采用重点法处理边界元法计算复杂边界条件时的角点问题。最后，在得到速度场之后，采用正则化快速多极子边界元法求解压力Poisson方程，得到计算流场的压力分布。本文利用Fortran语言实现计算程序的编写，计算程序实现了快速多极子三维涡方法和正则化快速多极子边界元法的各种功能。通过三个典型算例的数值模拟，验证了本文提出的混合三维涡方法的有效性和准确性，并确定多极子相关参数的取值范围。将该方法扩展应用到一低比转速Ns=148.8的导叶式混流泵内部非定常流动的数值模拟中。模拟混流泵在设计工况Qd，小流量工况0.75Qd和大流量工况1.25Qd的非定常流动。通过数值模拟结果与实验结果的对比，证实了该方法在计算模拟流体机械内部复杂非定常流动的有效性和可靠性。

Numerical simulations of the internal flow in fluid machinery are mostly based on the Eulerian framework. The three dimensional vortex methods, as a Lagrangian numerical method, have gradually attracted people's attention by the advantages in the calculation. Vortex method does not need to divide grids, so the numerical viscosity can be avoid in the calculation. At the same time, the vortex method is an adaptive method, which calculation region is focus on the region with high vorticity. So the vortex method can improve the computational efficiency and accuracy. For incompressible flow, the vorticity transport equation does not contain the pressure parameter, so the vorticity transport equation and the Poisson equation of pressure can be solved individually. In addition, the three dimensional vortex methods is easy for parallel computing from its theoretical basis, and it can effectively solve the problem of large scale flow field.Based on the traditional three-dimensional vortex methods, this paper proposes a new hybrid 3D vortex method. Firstly, the vorticity field is discrete by the vortex model, through the Lagrangian vorticity transport equation. We can track the changes in position and intensity of the discrete vortex elements by using the split step method proposed by Chorin for calculating the whole flow field. Unable to directly give the vorticity boundary condition, this paper uses the method of superposition of potential flow. As keeping the meshless characteristic of vortex method, the potential flow velocity field in order to satisfy no penetration condition can be solved by the boundary element method. By introducing a new vortex on the boundary in order to satisfy the no slip boundary condition. Computing the migration velocity of vortex element in Lagrange's framework, and the induced velocity of the discrete vortex elements can be obtained by the generalized Biot-Savart formula. The viscous diffusion terms in the near wall can be solved by the random walk method, and obtained by using particle strength exchange method in flow field. According to the calculation of the full rank matrix in boundary element method and induced velocity by vortex element with the large quantity and storage capacity, we adopt the fast multipole method. The strongly singular integral in the boundary element method can be solved by the regularization method. The multi points method is used for the corner problem. Finally, the pressure distribution of flow field can be solved individually by using the regularization fast multipole boundary element method.The hybrid 3D vortex method proposed in this paper is approved by the classical numerical simulation examples, and the ranges of the calculation parameters are determined. This method is applied to the simulation of the internal unsteady flow in a low specific speed mixed flow pump. The functions of the fast multipole 3D vortex method and regularization of fast multipole boundary element method are realized by Fortran language program. The Fortran program is used to calculate three conditions of the mixed flow pump in the design flow rate Qd, in off design flow rate 0.75Qd and 1.25Qd. Through the comparison between numerical results and experimental results, the validity of the proposed method is proved and the proposed method is suitable for calculating the complex internal unsteady flow in fluid machinery.