采用质点跟踪方法对物质输运方程平流项数值格式的改进

用数值模式对河口海岸地区的物质输运进行计算时，平流项的数值格式必须要能对物质浓度锋面进行正确处理，以避免产生过多的数值耗散或频散。本文中设计了一种在网格内设置一些质点并对质点进行跟踪的格式计算平流项。结果表明，质点跟踪格式在一维情形下无频散和几乎没有耗散，在二维情形下无频散和在水深变化剧烈的地方基本避免了垂向数值耗散。与其他数值格式的耗散性和频散性相比，本文中设计的数值格式明显地提高了物质输运方程中平流项的计算精度，在河口海洋物质输运的计算中具有较大的应用价值。

IMPROVEMENT IN NUMERICAL SCHEME ON THE ADVECTION TERM OF MASS TRANSPORT EQUATION USING PARTICLE-TRACING METHOD

When mass transport in the areas of estuary and coast is simulated, the numerical scheme of the advection term of mass transport equation should be designed correctly for the fronts of sharp concentration gradients to prevent ex-cessive numerical diffusion or dispersion.In this paper, the particle-tracing method, in which particles are initially set and then traced, is designed to improve the advection scheme.The results of our digital simulation show that the new method has no dispersion and almost no diffusion in one-dimensional case, and has no dispersion with tiny vertical diffusion in sharp-slope topography in two-dimensional case.Compared with other numerical schemes, this method has significantly higher calculation precision for the advection term, and should be recommended for simulating mass transport in estuary and coast.