Monte-Carlo方法求解水动力学方程的原理及实践

摘要

介绍Monte-Carlo方法的基本思想及求解Poisson方程的原理；利用Monte-Carlo方法及图论建立河网计算的随机游动模型，并应用于实际的大型河网中，取得了较好的结果.利用Monte-Carlo方法计算河网可以避免解大型的稀疏矩阵，计算简单、灵活.%The basic thinking about the Monte-Carlo Method and the principle for solving Poisson Equations are introduced. A random wandering model for the calculation of river networks is established by use of the Monte-Carlo Method and the graph theory, and the application of the model to large-scale river networks shows its good performance. By use of the Monte-Carlo Method calculation of large-scale matrixes can be avoided, thus, the calculation process is made simple and quick.