从理论上分析了颗粒流本构关系的最一般形式，及其在平面简单剪切流这一典型且常用的剪切流动条件下的本构关系。颗粒群受剪从极慢颗粒流动，低速颗粒流动，一直到快速颗粒流动的本构关系可以统一起来。利用试验资料，对颗粒在空气中受剪的本构关系进行了分析，很好地验证了理论分析结果。尤其是，理论分析及所有试验都表明在正应力和剪切应力表达式中存在流速梯度的线性项，揭示出在颗粒流中还存在颗粒的相对滑动及相互挤压作用，该项与普通流体的线性粘滞应力类似，但有根本的不同。

On the basis of traditional particle-in-cell methods, a particle model has been developed to simulate flow over large areas. Under the assumption that the fluid medium is an assembly of many small, independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions. In the formulation used, only two forces are involved. One is the hydrostatic force arising from the accumulation of different numbers of particles at different locations. The other is a friction force that varies inversely with flow depth and quadratically with particle velocity and bed roughness. The velocity and spatial positions of all particles are averaged at fixed grid points to obtain the overall flow behavior. The particle model is demonstrated through an application to a documented 1954 flood in the Jingjiang River flood diversion area in Hubei, China. The flood lasted 300 h, with the total discharge volume being 4 billion m3. Good agreement between computed and observed water levels was obtained. Convergence of the method is demonstrated by repeatedly doubling the number of particles employed in the computation until there is little change between simulations.

用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用，用修正的BGK模型描述粒间碰撞效应，建立了封闭的颗粒相PDF输运方程。运用Chapmar-Enskog迭代法求得方程的二阶近似解，获得颗粒相脉动速度二阶矩和三阶矩闭合关系。模型与颗粒流模型相容，与液相湍流闭合模型是否相容依赖于扩散模型的具体形式，并据此比较了不同的涡-颗粒作用模型。模型与二维明渠流轻质沙和天然沙试验资料符合很好。表明细小粒径颗粒能够充分跟随水流运动；大粒径颗粒的相间平均速度差和壁面滑移速度明显，近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流，并存在一定程度的颗粒碰撞效应。