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.

A discrete element model (DEM) is developed for investigation of the dynamic behavior of sand grains, in which the motion of individual grains is considered. The DEM has been used for simulating 9000 grains" motion blown by wind, resulting in ripples and saltating paths. Exchange between saltation and creep along the surface is also calculated, which is helpful for revealing the intrinsic mechanism of ripple formation. A critical event in the trajectory of sand grain saltating in the air is its interaction with the surface. As another application of DEM, the numerical experiment of a sand bed impacted by a single grain traveling at 8ms-1 and I 1.5 is performed to quantitatively evaluate the splash process. A normalized Maxwellian distribution function f(uy)=a ucy exp(-b. uyd) is proposed for the vertical velocity distribution of splashed grains, where the parameters a, b. c. and d can be regressed from the vertical velocity component of sahating grains. Generally, the vertical velocity of saltating grains fits the Maxwellian function well, with the correlation coefficients larger than 0.8. The result also shows that the restitution and surface friction coefficients of grains have negligible influence on the Maxwellian function. Therefore, the DEM can simulate sand movement and offer more detailed information as to what happens inside the flow. which could be applied in a wider suitable range in comparison with previous models.