We study the validity of the dissipative Aw–Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behavior. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw–Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.

我们研究耗散 Aw-Rascle 系统作为行人动力学宏观模型的有效性。该模型使用拥塞项（奇异扩散项）来强制人群密度的容量限制，同时诱导转向行为。此外，我们引入了半隐式、结构保持和渐近保持的数值格式，可以有效地处理模型的数值求解。我们对耗散 Aw-Rascle 系统进行了一维和二维的首次数值模拟。我们证明了该方案在解决一系列数值实验方面的效率，并验证了该模型，最终表明它正确地捕获了行人流的基本图。