 An asymptotic preserving and energy stable scheme for the Euler system with congestion constraintK.R. Arun, A. Krishnamurthy and H. Maharna Applied Mathematics and Computation, 2025, vol. 495, issue C Abstract: In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form 0≤ϱ<1, and the scaling introduces a small parameter ε in order to control the stiffness of the density constraint. As ε→0, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property. Keywords: Isentropic Euler system; Congestion pressure; Singular limit; Staggered finite volume method; Asymptotic preserving; Energy stability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000335 DOI: 10.1016/j.amc.2025.129306 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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