Numerical simulations of the Euler system with congestion constraint

Abstract

In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in [1, 3] with the constraint introduced into the system by a singular pressure law, which causes the transition of different asymptotic dynamics between different regions. To overcome these difficulties, we adapt and implement two asymptotic preserving (AP) schemes originally designed for low Mach number limit [2,4] to our model. These schemes work for the different dynamics and capture the transitions well. Several numerical tests both in one dimensional and two dimensional cases are carried out for our schemes.

References in corpus (2)

• All speed scheme for the low mach number limit of the Isentropic Euler equation
• Congestion in a macroscopic model of self-driven particles modeling gregariousness

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• Soft congestion approximation to the one-dimensional constrained Euler equations
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• Free/Congested Two-Phase Model from Weak Solutions to Multi-Dimensional Compressible Navier-Stokes Equations
• Existence and stability of partially congested propagation fronts in a one-dimensional Navier-Stokes model
• Compression Effects in Heterogeneous Media
• Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains