宏观流体力学仿真在人群运动数学建模中的应用——以2019年MCM/ICM卢浮宫游客疏散问题为例

人群运动与流体运动有许多相似性.本文旨在借助FLOW3D模型模拟人群运动,为解决人群疏散问题提供定性方案.以2019年数学建模美赛d题为例,首先根据人群运动规划全局矢量场的研究结果对模型进行预处理,建立行人运动的宏观流体力学模型.运用FLOW3D模型对模型进行仿真模拟,水体的仿真运动受完整的N-S方程控制,使用RNG湍流模型模拟动态碰撞情况.最后对流体运动结果进行定性分析,得到人群的宏观运动情况,并附图像说明.

There are many similarities between crowd movement and fluid movement.This paper aims to simulate crowd movement with FLOW3D model and provide a qualitative solution for crowd evacuation.Taking the problem D of MCM\ICM 2019 as an example,the macroscopic hydrodynamic model of pedestrian motion was firstly preprocessed according to the research results of the global vector field of crowd motion planning.FLOW3D model is used to simulate the model.The water simulation movement was controlled by the N-S equation,and the RNG turbulence model was used to simulate the dynamic collision.Finally,by qualitative analysis of the fluid motion results,the macroscopic motion of the crowd was obtained with the image description attached.