Singular limit behaviour: rescaled congestion, $\varepsilon\phi$.

Section 4.1.3; Figure 13.

Rescaled congestion, $\varepsilon\phi$. Second-order scheme. Periodic boundary conditions. $x\in(0,1)$. $\varepsilon \in \{10^{-2},10^{-3},10^{-4},10^{-5}\}$.

$\Delta t=\Delta x/16$.

$M=32$, $\Delta x= 2^{-5}$.

$M=64$, $\Delta x= 2^{-6}$.

$M=128$, $\Delta x= 2^{-7}$.

$M=256$, $\Delta x= 2^{-8}$.

$M=512$, $\Delta x= 2^{-9}$.

$M=1024$, $\Delta x= 2^{-10}$.

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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