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Reconstruction Techniques and Finite Volume Schemes for Hyperbolic Conservation Laws

Artebrant, Robert LU (2006) In Doctoral Theses in Mathematical Sciences
Abstract
This thesis concerns the numerical



approximation of the solutions to



hyperbolic conservation laws.



In particular the research work focuses



on reconstruction techniques;



the reconstruction being the key



ingredient in modern finite volume



schemes aiming to increase spatial



order of accuracy. To better conform



to the nature of the solutions to



the hyperbolic problems, the



reconstructing function is non-polynomial; in contrast to other reconstructions this allows us to have a continuous function representation, possibly having an... (More)
This thesis concerns the numerical



approximation of the solutions to



hyperbolic conservation laws.



In particular the research work focuses



on reconstruction techniques;



the reconstruction being the key



ingredient in modern finite volume



schemes aiming to increase spatial



order of accuracy. To better conform



to the nature of the solutions to



the hyperbolic problems, the



reconstructing function is non-polynomial; in contrast to other reconstructions this allows us to have a continuous function representation, possibly having an extremum, within each spatial cell without limiting slopes. The flexible and simple to use reconstruction enables in a novel manner the derivation of schemes that efficiently combine the properties of accuracy, resolution and damping of spurious oscillations. Furthermore, applicability of the reconstruction is not restricted to Cartesian meshes as demonstrated by numerically solving the Euler equations of gas dynamics on triangular meshes in the finite volume context. (Less)
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author
supervisor
opponent
  • Professor Marquina, Antonio, Departmento of Matematica Aplicada, Universidad de Valencia, Valencia, Spain.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
numerical analysis, Computer science, high order reconstruction, Conservation law, finite volume method, Datalogi, control, systems, kontroll, numerisk analys, system
in
Doctoral Theses in Mathematical Sciences
pages
160 pages
publisher
LUND UNIVERSITY Numerical Analysis Centre for Mathematical Sciences
defense location
Room M:E, M-building, Ole Römers väg 1, Lund Institute of Technology
defense date
2006-03-10 10:15:00
ISSN
1404-0034
ISBN
978-91-628-6748-5
91-628-6748-2
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
c4e052e2-498a-4147-916e-cf80c64d9ef6 (old id 546277)
date added to LUP
2016-04-01 15:27:37
date last changed
2019-05-21 13:42:17
@phdthesis{c4e052e2-498a-4147-916e-cf80c64d9ef6,
  abstract     = {This thesis concerns the numerical<br/><br>
<br/><br>
approximation of the solutions to<br/><br>
<br/><br>
hyperbolic conservation laws.<br/><br>
<br/><br>
In particular the research work focuses<br/><br>
<br/><br>
on reconstruction techniques;<br/><br>
<br/><br>
the reconstruction being the key<br/><br>
<br/><br>
ingredient in modern finite volume<br/><br>
<br/><br>
schemes aiming to increase spatial<br/><br>
<br/><br>
order of accuracy. To better conform<br/><br>
<br/><br>
to the nature of the solutions to<br/><br>
<br/><br>
the hyperbolic problems, the<br/><br>
<br/><br>
reconstructing function is non-polynomial; in contrast to other reconstructions this allows us to have a continuous function representation, possibly having an extremum, within each spatial cell without limiting slopes. The flexible and simple to use reconstruction enables in a novel manner the derivation of schemes that efficiently combine the properties of accuracy, resolution and damping of spurious oscillations. Furthermore, applicability of the reconstruction is not restricted to Cartesian meshes as demonstrated by numerically solving the Euler equations of gas dynamics on triangular meshes in the finite volume context.},
  author       = {Artebrant, Robert},
  isbn         = {978-91-628-6748-5},
  issn         = {1404-0034},
  language     = {eng},
  publisher    = {LUND UNIVERSITY Numerical Analysis Centre for Mathematical Sciences},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Reconstruction Techniques and Finite Volume Schemes for Hyperbolic Conservation Laws},
  year         = {2006},
}