A Particle-tracing Method And Its Application

The numerical scheme of the advection term should be designed correctly for the fronts of sharp concentration gradients to prevent excessive numerical diffusion or dispersion when calculating mass transport in the areas of estuary and coast. Some basic schemes, such as central differencing, upwind and Lax-wendroff, are either highly diffusive or extremely dispersive. Eulerian-Lagrangian Method (ELM) can prevent the dispersion while lower the diffusion, but its diffusion is still considerable, so it is necessary to be further improved. In addition, if the horizontal interpolation process was taken in a a plain, then the bended σ plain would make the interpolation sources unreasonable. So in this paper, first, the ELM is improved by taking the interpolation process under absolute coordinates, so that the horizontal interpolation could be taken in a horizontal plain of the same altitude, thus the problem of unreasonable interpolation sources is prevented. Then, the Particle-tracing Method is designed, which calculates the advection term by setting some particles in the grid cells and tracing them. Without repeated interpolations such as in ELM, the Particle-tracing Method reduces the numerical diffusion quite a lot. The low diffusion of the Particle-tracing Method is shown in a one-dimensional experiment and a two-dimensional one, while the improved ELM performs better than the original ELM in the two-dimensional experiment. Finally, under the three-dimensional ECOM model, the Particle-tracing Method is applied to the numerical modeling of the Changjiang Estuary sewage diffusion. In this modeling, the Particle-tracing Method is again compared with the improved ELM by calculating the concentration of COD. The result shows that the Particle-tracing Method is not only less diffusive, but also more conservative. Meanwhile, by modeling the sewage diffusion, it is found that the range of the Changjiang Estuary sewage diffusion area can reach the East Chongming Bank, the Deep water Channel, and the Nanhui Bank, while the COD concentration near Meimaosha is especially high so that the sewage diffusion constitutes a threat to the water quality of Meimaosha area.