Crowd collision and model instability.

Section 4.3; Figure 9.

Periodic (on the left and right boundaries) and no-flux (on the remaining) boundary conditions. $x\in(0,1)$, $y\in(0,1.5)$, $t = 0.5$.

Second-order scheme. $M_x=512$, $M_y=256$, $\Delta x= \Delta y=2^{-9}$, $\Delta t=\Delta x/16$.

$\varepsilon = 1.0$. Crowd density, $\rho$.

$\varepsilon = 1.0$. Desired momentum ($x$-component), $q_1$.

$\varepsilon = 0.1$. Crowd density, $\rho$.

$\varepsilon = 0.1$. Desired momentum ($x$-component), $q_1$.

$\varepsilon = 0.01$. Crowd density, $\rho$.

$\varepsilon = 0.01$. Desired momentum ($x$-component), $q_1$.

$\varepsilon = 0.001$. Crowd density, $\rho$.

$\varepsilon = 0.001$. Desired momentum ($x$-component), $q_1$.

$\varepsilon = 0.0001$. Crowd density, $\rho$.

$\varepsilon = 0.0001$. Desired momentum ($x$-component), $q_1$.

Pedestrian models with congestion effects

Pedro Aceves-Sánchez · Rafael Bailo · Pierre Degond · Zoé Mercier
Mathematical Models and Methods in Applied Sciences, 34 (6), 2024.


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