Congestion and the numerical fundamental diagram: medium narrowing, $\varepsilon = 0.025$.

Section 4.2; Figure 5.

Influx, outflux, and no-flux boundary conditions (respectively, on the left, right, and remaining boundaries). $x\in(0,1)$, $y\in(0,1.5)$. $\varepsilon = 0.025$.

Second-order scheme. $M_x=128$, $M_y=64$, $\Delta x= \Delta y=2^{-7}$, $\Delta t=\Delta x/4$.

$\rho_{\text{In}}= 0.1$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.1$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.2$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.2$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.3$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.3$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.4$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.4$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.5$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.5$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.6$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.6$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.7$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.7$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.8$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.8$. Flux ($x$-component), $J_1$.

$\rho_{\text{In}}= 0.9$. Crowd density, $\rho$.

$\rho_{\text{In}}= 0.9$. Flux ($x$-component), $J_1$.

Pedestrian models with congestion effects

Pedro Aceves-Sánchez · Rafael Bailo · Pierre Degond · Zoé Mercier
Mathematical Models and Methods in Applied Sciences, 2024 (to appear).


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