In this paper, we present two computational methods for performing simulations of pollution propagation described by advection-diffusion equations. The first method employs graph grammars to describe the generation process of the computational mesh used in simulations with the meshless solver of the three-dimensional finite element method. The graph transformation rules express the three-dimensional Rivara longest-edge refinement algorithm. This solver is used for an exemplary application: performing three-dimensional simulations of pollution generation by the coal-burning power plant and its propagation in the city of Longyearbyen, the capital of Spitsbergen. The second computational code is based on the Physics Informed Neural Networks method. It is used to calculate the dissipation of the pollution along the valley in which the city of Longyearbyen is located. We discuss the instantiation and execution of the PINN method using Google Colab implementation. We discuss the benefits and limitations of the PINN implementation.

翻译：本文提出了两种用于模拟由对流-扩散方程描述的污染传播过程的计算方法。第一种方法采用图语法来描述计算网格的生成过程，该网格用于结合三维有限元法的无网格求解器进行仿真。图转换规则表达了三维Rivara最长边细化算法。该求解器用于一个示例应用：模拟燃煤电厂产生的污染及其在斯匹次卑尔根岛首府朗伊尔城的三维传播过程。第二种计算代码基于物理信息神经网络方法，用于计算污染沿朗伊尔城所在山谷的扩散过程。我们讨论了使用Google Colab实现PINN方法的实例化与执行过程，并分析了该PINN实现的优势与局限性。