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Numerical identification of constitutive functions in scalar nonlinear convection-diffusion equations with application to batch sedimentation

Diehl, Stefan LU (2015) In Applied Numerical Mathematics 95(Available online 13 April 2014). p.154-172
Abstract
A fast and simple method for the identification of nonlinear constitutive functions in scalar convection–diffusion equations is presented. No a priori information is needed on the form of the constitutive functions, which are obtained as continuous piecewise affine functions. Accurate and frequent measurements in space and time are required. Synthetic data of batch sedimentation of particles in a liquid and traffic flow are chosen as examples where a convective flux function and a function modelling compression are identified. Real data should first undergo a denoising procedure, which is also presented. It consists of a sequence of convex optimization problems, whose constraints originate from fundamental physical properties. The... (More)
A fast and simple method for the identification of nonlinear constitutive functions in scalar convection–diffusion equations is presented. No a priori information is needed on the form of the constitutive functions, which are obtained as continuous piecewise affine functions. Accurate and frequent measurements in space and time are required. Synthetic data of batch sedimentation of particles in a liquid and traffic flow are chosen as examples where a convective flux function and a function modelling compression are identified. Real data should first undergo a denoising procedure, which is also presented. It consists of a sequence of convex optimization problems, whose constraints originate from fundamental physical properties. The methodology is applied on data from a batch sedimentation experiment of activated sludge in wastewater treatment. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Applied Numerical Mathematics
volume
95
issue
Available online 13 April 2014
pages
154 - 172
publisher
Elsevier
external identifiers
  • wos:000356733600012
  • scopus:84929708068
ISSN
0168-9274
DOI
10.1016/j.apnum.2014.04.002
language
English
LU publication?
yes
id
640e3d72-457a-4029-ba66-e113d5d9cd1d (old id 5268494)
date added to LUP
2015-04-27 10:44:55
date last changed
2017-10-22 03:15:21
@article{640e3d72-457a-4029-ba66-e113d5d9cd1d,
  abstract     = {A fast and simple method for the identification of nonlinear constitutive functions in scalar convection–diffusion equations is presented. No a priori information is needed on the form of the constitutive functions, which are obtained as continuous piecewise affine functions. Accurate and frequent measurements in space and time are required. Synthetic data of batch sedimentation of particles in a liquid and traffic flow are chosen as examples where a convective flux function and a function modelling compression are identified. Real data should first undergo a denoising procedure, which is also presented. It consists of a sequence of convex optimization problems, whose constraints originate from fundamental physical properties. The methodology is applied on data from a batch sedimentation experiment of activated sludge in wastewater treatment.},
  author       = {Diehl, Stefan},
  issn         = {0168-9274},
  language     = {eng},
  number       = {Available online 13 April 2014},
  pages        = {154--172},
  publisher    = {Elsevier},
  series       = {Applied Numerical Mathematics},
  title        = {Numerical identification of constitutive functions in scalar nonlinear convection-diffusion equations with application to batch sedimentation},
  url          = {http://dx.doi.org/10.1016/j.apnum.2014.04.002},
  volume       = {95},
  year         = {2015},
}