Hyperbolic Conservation Laws with Relaxation Terms: A Theoretical and Numerical Study
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 masters 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 ChapmanEnskog 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
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.
ntnudaim:6477, MTFYMA fysikk og matematikk, Teknisk fysikk
IdentifiersURN: urn:nbn:no:ntnu:diva-14540Local ID: ntnudaim:6477OAI: oai:DiVA.org:ntnu-14540DiVA: diva2:455353
Simonsen, Ingve, ProfessorFlåtten, ToreMunkejord, Svend Tollak