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Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation

Careaga, Julio LU and Diehl, Stefan LU (2020) In Mathematical Methods in the Applied Sciences 43(7). p.4530-4557
Abstract

Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
hindered settling, inverse problem, Kynch constitutive assumption, method of characteristics, nonconvex flux function, nonlinear hyperbolic PDE, separation process
in
Mathematical Methods in the Applied Sciences
volume
43
issue
7
pages
28 pages
publisher
John Wiley and Sons Inc.
external identifiers
  • scopus:85083534730
ISSN
0170-4214
DOI
10.1002/mma.6212
language
English
LU publication?
yes
id
640a1f65-0a63-4f92-a8ce-906e058a3dbc
date added to LUP
2020-04-29 08:32:14
date last changed
2020-10-07 06:58:05
@article{640a1f65-0a63-4f92-a8ce-906e058a3dbc,
  abstract     = {<p>Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data.</p>},
  author       = {Careaga, Julio and Diehl, Stefan},
  issn         = {0170-4214},
  language     = {eng},
  number       = {7},
  pages        = {4530--4557},
  publisher    = {John Wiley and Sons Inc.},
  series       = {Mathematical Methods in the Applied Sciences},
  title        = {Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation},
  url          = {http://dx.doi.org/10.1002/mma.6212},
  doi          = {10.1002/mma.6212},
  volume       = {43},
  year         = {2020},
}