一种自适应时间步长的场地地表污染扩散元胞自动机仿真模型

针对传统扩散模型难以动态模拟地表污染物时空不均匀扩散过程的问题，本文提出一种基于元胞自动机模型的污染物地表扩散仿真模型，在综合考虑地表高差及粗糙度对污染物扩散过程影响的基础上，确定了不规则污染场地的元胞边界条件、划分了元胞空间、提出了一种降雨和非降雨条件下污染物扩散流速计算方法，基于分子扩散建立了地表污染扩散模型演变规则。为更好模拟地表污染物扩散情况，本文提出了一种污染物随坡度和质量衰减的元胞自适应时间步长调整算法，该算法能够动态调整元胞自动机的时间步长，防止固定时间步长在污染物快速扩散时错过细节，而缓慢扩散时消耗计算资源。实验设计了降雨和非降雨两种情形对污染物随时间扩散的过程进行仿真与分析。实验结果表明，不同下垫面对污染物扩散速度有很大的影响，污染物在糙率为0.012的水泥地表上的扩散速度约为其在糙率为0.035的一般性土壤地表上的2.7倍；降雨强度和时长能够加快污染物的扩散，且扩散速度随着降雨曲线变化而改变，并在雨强峰值附近达到最大；污染物扩散服从坡度分布特征，且随着时间变化，高污染区域范围和污染物浓度差异渐渐变小，并在一段时间后，浓度变化渐渐趋于平稳；自适应时间步长演变算法能够较好地体现一次演变过程中污染物扩散在不同邻域元胞方向上的细微时间差异，提高污染物时空分布的计算精度。

A Cellular Automata Simulation Model of Site Surface Pollution Diffusion with Adaptive Time Step

Aiming at the problem that it is difficult for traditional pollution simulation models to simulate the uneven diffusion process of surface pollutants dynamically in time and space, this paper proposes a surface pollutants diffusion simulation model based on cellular automata model. In this paper, surface slope and surface roughness are considered as the main factors affecting the diffusion process of pollutants. Based on the irregular contaminated site area, the boundary conditions of the cell were firstly determined to obtain the whole cell space, and then the whole cell space was divided into regular cells. After that, a method for calculating the diffusion velocity of pollutants under rainfall and non-rainfall conditions was proposed. Finally, based on the molecular diffusion rules, The evolution rules of surface pollutant diffusion model under rainfall and non-rainfall conditions were established. For better simulating surface pollutant diffusion, this paper proposes a cellular adaptive time step adjustment algorithm, in which pollutant quality decay with surface slope and pollutant gravity. This algorithm can adjust the cellular automata time step automatically and dynamically, so as to prevent cellular automata model with fixed time steps from missing details when pollution spread quickly and computing resources wasting when they spread slowly. In this paper, two experiments which consider rainfall and non-rainfall conditions respectively are designed to simulate the diffusion process of pollutants over time. The experimental results show that different underlying layers have a great influence on the diffusion rate of pollutants; the diffusion velocity of pollutants on the cement surface with a roughness of 0.012 is about 2.7 times of that on a general soil surface with a roughness of 0.035; under rainfall conditions, the pollution diffusion velocity increases with the increase of rainfall intensity and duration, the diffusion velocity changes with the change of rainfall curve, and reaches the maximum near the peak of rainfall intensity; the pollution diffusion simulation results obey the slope distribution characteristics of the site; with the change of time, the range of high pollution area gradually decreases, and the difference in pollutant concentration between adjacent locations also gradually decreases, and after a period of time, this change gradually becomes stable; in the process of a model evolution, surface pollutants will have subtle differences in diffusion time in different neighborhood cell directions, and the adaptive time step evolution algorithm can better reflect this difference, so it can better improve the calculation accuracy of spatial and temporal distribution of pollutants.