Transport of congestion in two-phase compressible/incompressible flows
File(s)
Published version
Author(s)
Degond, PAA
Minakowski, Piotr
Zatorska, Ewelina
Type
Journal Article
Abstract
We study the existence of weak solutions to the two-phase fluid model with congestion constraint. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two phases. The congested regime appears when the density in the uncongested regime achieves a threshold value that describes the comfort zone of individuals. This quantity is prescribed initially and transported along with the flow. We prove that this system can be approximated by the fully compressible Navier–Stokes system with a singular pressure, supplemented with transport equation for the congestion density. We also present the application of this approximation for the purposes of numerical simulations in the one-dimensional domain.
Date Issued
2018-08-01
Date Acceptance
2018-02-05
Citation
Nonlinear Analysis: Real World Applications, 2018, 42, pp.485-510
ISSN
1468-1218
Publisher
Elsevier
Start Page
485
End Page
510
Journal / Book Title
Nonlinear Analysis: Real World Applications
Volume
42
Copyright Statement
© 2018 The Authors. Published by Elsevier Ltd. This
is an open access article under the CC BY licence
(http://creativecommons.org/licenses/by/4.0/).
is an open access article under the CC BY licence
(http://creativecommons.org/licenses/by/4.0/).
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/M006883/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Constrained fluid model
Navier-Stokes equations
Free boundary
Singular pressure
Renormalized transport
NAVIER-STOKES EQUATIONS
TRAFFIC JAMS
ENTROPY TRANSPORT
PEDESTRIAN FLOW
WEAK SOLUTIONS
MODEL
CROWDS
STABILITY
EXISTENCE
EVOLUTION
math.AP
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2018-02-26