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Conservative logarithmic reconstructions and finite volume methods

Artebrant, Robert LU and Schroll, Achim LU (2005) In SIAM Journal on Scientific Computing 27(1). p.294-314
Abstract
A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
high-order reconstruction, conservation law, finite volume method
in
SIAM Journal on Scientific Computing
volume
27
issue
1
pages
294 - 314
publisher
SIAM Publications
external identifiers
  • wos:000232354900014
  • scopus:33144480893
ISSN
1064-8275
DOI
10.1137/03060240X
language
English
LU publication?
yes
id
53a11d0b-686b-4031-bbdd-6454d060b30d (old id 220526)
date added to LUP
2007-08-07 11:05:03
date last changed
2017-01-01 07:03:26
@article{53a11d0b-686b-4031-bbdd-6454d060b30d,
  abstract     = {A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.},
  author       = {Artebrant, Robert and Schroll, Achim},
  issn         = {1064-8275},
  keyword      = {high-order reconstruction,conservation law,finite volume method},
  language     = {eng},
  number       = {1},
  pages        = {294--314},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Scientific Computing},
  title        = {Conservative logarithmic reconstructions and finite volume methods},
  url          = {http://dx.doi.org/10.1137/03060240X},
  volume       = {27},
  year         = {2005},
}