The random-walk method is inherently simple and numerically stable. However, when used in hydro-environmental analyses, most of the existing random-walk methods ignore the influence of the non-uniform water depth and only consider the transport of inert materials, hence the inability of modelling biochemical reactions. In addition, the existing applications mainly focus on instantaneous-release problems, where a fixed number of particles move in the computational domain. This paper first presents examples to showcase the capability of a newly-developed random-walk model in simulating the continuous sources of non-conservative substances. Then, the method is applied to examine the BOD-DO balance along a hypothetical river. The predictions agree well with analytical solutions. Finally, the developed model is used to study the pollutant transport in the Thames Estuary. The current model is illustrated to be able to accurately predict the interaction between multiple pollutants in real-world situations with uneven bathymetry and extensive intertidal floodplains.

随机游走方法本质上简单且数值稳定。但是，当用于水环境分析时，大多数现有的随机游走方法都忽略了水深不均匀的影响，只考虑了惰性物质的运输，因此无法对生化反应进行建模。此外，现有的应用程序主要关注瞬时释放问题，其中固定数量的粒子在计算域中移动。本文首先提供示例，以展示新开发的随机游走模型在模拟非保守物质连续来源中的功能。然后，将该方法应用于检查一条假设河流的BOD-DO平衡。这些预测与分析解决方案非常吻合。最后，所开发的模型用于研究泰晤士河口的污染物迁移。说明了当前模型，该模型能够通过不均匀的测深和大量的潮间带洪泛区来准确预测现实世界中多种污染物之间的相互作用。