Reconstruction Techniques and Finite Volume Schemes for Hyperbolic Conservation Laws
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/546277
- author
- Artebrant, Robert LU
- supervisor
- opponent
-
- Professor Marquina, Antonio, Departmento of Matematica Aplicada, Universidad de Valencia, Valencia, Spain.
- organization
- publishing date
- 2006
- 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}},
keywords = {{numerical analysis; Computer science; high order reconstruction; Conservation law; finite volume method; Datalogi; control; systems; kontroll; numerisk analys; system}},
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}},
}