Change search
ReferencesLink to record
Permanent link

Direct link
Hyperbolic Conservation Laws with Relaxation Terms: A Theoretical and Numerical Study
Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, Department of Physics.
2011 (English)MasteroppgaveStudent thesis
Abstract [en]

Hyperbolic relaxation systems is an active field of research, with a large number of applications in physical modeling. Examples include models for traffic flow, kinetic theory and fluid mechanics. This master’s thesis is a numerical and theoretical analysis of such systems, and consists of two main parts: The first is a new scheme for the stable numerical solution of hyperbolic relaxation systems using exponential integrators. First and second-order schemes of this type are derived and some desirable stability and accuracy properties are shown. The scheme is also used to solve a granular-gas model in order to demonstrate the practical use of the method. The second and largest part of this thesis is the analysis of the solutions to 2 × 2 relaxation systems. In this work, the link between the the sub-characteristic condition and the stability of the solution of the relaxation system is discussed. In this context, the sub-characteristic condition and the dissipativity of the Chapman–Enskog approximation are shown to be equivalent in both 1-D and 2-D. Also, the dispersive wave dynamics of hyperbolic relaxation systems is analyzed in detail. For 2 × 2 systems, the wave-speeds of the individual Fourier-components of the solution are shown to fulfill a transitional sub-characteristic condition. Moreover, the transition is monotonic in the variable ξ = kε, where ε is the relaxation time of the system and k is the wave-number. A basic 2 × 2 model is used both as an example-model in the analytical discussions, and as a model for numerical tests in order to demonstrate the implications of the analytical results.

Place, publisher, year, edition, pages
Institutt for fysikk , 2011. , 101 p.
Keyword [no]
ntnudaim:6477, MTFYMA fysikk og matematikk, Teknisk fysikk
URN: urn:nbn:no:ntnu:diva-14540Local ID: ntnudaim:6477OAI: diva2:455353
Available from: 2011-11-09 Created: 2011-11-09

Open Access in DiVA

fulltext(1008 kB)635 downloads
File information
File name FULLTEXT01.pdfFile size 1008 kBChecksum SHA-512
Type fulltextMimetype application/pdf
cover(47 kB)18 downloads
File information
File name COVER01.pdfFile size 47 kBChecksum SHA-512
Type coverMimetype application/pdf

By organisation
Department of Physics

Search outside of DiVA

GoogleGoogle Scholar
Total: 635 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 48 hits
ReferencesLink to record
Permanent link

Direct link