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 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.
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.
| Original language | English |
|---|---|
| Qualification | Doctor |
| Awarding Institution |
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| Supervisors/Advisors |
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| Award date | 2006 Mar 10 |
| Publisher | |
| ISBN (Print) | 978-91-628-6748-5, 91-628-6748-2 |
| Publication status | Published - 2006 |
Bibliographical note
Defence detailsDate: 2006-03-10
Time: 10:15
Place: Room M:E, M-building, Ole Römers väg 1, Lund Institute of Technology
External reviewer(s)
Name: Marquina, Antonio
Title: Professor
Affiliation: Departmento of Matematica Aplicada, Universidad de Valencia, Valencia, Spain.
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The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)
Subject classification (UKÄ)
- Mathematics
Free keywords
- numerical analysis
- Computer science
- high order reconstruction
- Conservation law
- finite volume method
- Datalogi
- control
- systems
- kontroll
- numerisk analys
- system