两相流模型能够较为准确地描述水沙两相间的相互作用，揭示水沙运动机理。构建高精度、适用性强的水沙两相流模型对于完善泥沙运动理论、解决工程泥沙问题有重要的意义。本文旨在完善和发展水沙两相流数学模型，基于Eulerian-Lagrangian观点构建了一个适用于悬移质泥沙运动的颗粒轨道模型；基于Eulerian-Eulerian观点构建了一个可用于大涡模拟的双流体模型，并引入光滑粒子流体动力学（SPH）方法进行求解。 论文构建的Eulerian-Lagrangian两相流模型采用包含泥沙体积浓度的雷诺时均控制方程与k-ε紊流模型描述水相运动。视泥沙为分散介质，将泥沙颗粒的运动速度分解为时均流速与脉动速度，采用运动方程计算颗粒时均流速的变化，耦合涡相干模型（EIM）描述泥沙颗粒在紊动水体作用下的脉动。考虑尾流对颗粒紊动的增强效应修正涡相干模型以提高模型模拟悬移质泥沙紊动扩散的精度。基于低含沙浓度假设，简化两相控制方程，得到适用于低含沙水流悬移质输沙问题的Eulerian-Lagrangian两相流模型。将模型应用于二维明渠恒定均匀流悬移质输沙，计算了不同的泥沙粒径条件下悬移质相对浓度垂向分布，讨论了粒径对泥沙扩散系数的影响。结果显示，考虑尾流对颗粒紊动增强效应的Eulerian-Lagrangian模型能够准确模拟较宽粒径范围内的悬移质泥沙的紊动扩散。 论文构建的基于SPH方法的双流体模型对连续介质假设下推导的体积平均控制方程组进行空间滤波，采用质量浓度加权的Favre平均得到空间平均的两相控制方程，采用Smagorinsky公式计算亚粒子应力。考虑两相相间作用力、泥沙颗粒粒间作用力以及泥沙对水相亚粒子应力的影响，模型能够较全面地反映水沙两相的相互作用。将含沙水流离散成一组SPH粒子，粒子以水相速度运动并携带两相物理信息。将两相控制方程改写为粒子的运动方程及其携带的物理量控制方程，并采用SPH方法离散求解。将双流体模型应用于静水中抛泥问题，讨论泥沙云团的宽度、下沉速度及浓度分布随泥沙粒径与云团初始体积的变化规律。结果显示，本文构建的双流体模型能够准确描述泥沙云团的运动特性，适用于水沙两相流问题的研究。

The importance to develop an accurate and generally applicable two-phase flow model for sediment-laden flow has been emphasized ever-increasingly in the past decades. In the present study, an Eulerian-Lagrangian two-phase flow model is improved for suspended sediment, and an Eulerian-Eulerian two-fluid model is developed for large eddy simulations of sediment laden flows with the Smoothed Particle Hydrodynamics (SPH) method applied. In the improved Eulerian-Lagrangian model, the Reynolds averaged Navier-Stokes equations together with the k-ε turbulence model are applied to the water phase. In the RANS equations and equations for k and ε, sediment volume concentration is included to take into account the effect of sediment on the water. In the model, the solid phase is regarded as a dispersed phase, and the velocity of a sand particle is divided into a time-averaged and a fluctuating term. The time-averaged velocity of a sand particle is computed by the equation of motion, and the fluctuating term of the sand velocity due to the turbulent flow is evaluated by the Eddy Interaction Model (EIM). The EIM is enhanced considering the effect of the wake behind the particle to improve the accuracy of the Eulerian-Lagrangian model in simulating the suspension of sediment. The Eulerian-Lagrangian model is simplified for suspended sediment in dilute flows, and the simplified model is applied to sediment suspension under steady and uniform flow condition in a two-dimensional open channel. The profiles of sediment concentration under different sand diameter conditions are compared, and the effect of sand diameter on sediment turbulent dispersion coefficient is studied. It is shown that the Eulerian- Lagrangian two-phase flow model coupled with the enhanced EIM performs very well in simulating the suspension of sediment under more general conditions of particle size. In the developed SPH two-fluid model, the governing equations of the two phases are obtained by spatially filtering the Favre averaged basic equations. The Smagorinsky model is used to compute the sub-particle scale (SPS) stress of the two phases, and it is assumed that the Smagorinsky coefficient of the sediment phase equals to that of the water. The model includes the drag force for the interaction force between the two phases and relates the viscosity of the solid phase to inter-granular stress. The effect of sediment on the sub-particle scale turbulence is also modeled with a correction function of sediment concentration added to the formula of the flow eddy viscosity. The sediment-laden flow is divided into SPH particles, which move with the water velocity and carry the quantities of sediment concentration, sediment velocity, and water mass concentration. The spatially filtered governing equations are rewritten into SPH forms, and formulated and solved using the SPH method. The Eulerian-Eulerian two-fluid model is applied to sediment dumping, and the variation of the width, settling velocity, and concentration of the sand cloud is studied. It is concluded from the comparison of computed results with measured data that the developed SPH two-fluid model performs well in simulating the motion of the sand cloud.