Particle model for simulating flow over large areas. technical note

TLDR: In this article, a particle-in-cell model was 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.

Abstract: 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 hours, with the total discharge volume being 4 billion cu m. 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 little change was found between simulations.