Disputas: Adrian Montgomery Ruf
M.Sc. Adrian Montgomery Ruf ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.
Numerical methods for nonlinear conservation laws
Adrian Montgomery Ruf
Tid og sted for prøveforelesning
Professor Christian Rohde, Institute of Applied Analysis and Numerical Simulation
Professor Anders Szepessy, KTH
Professor Fred Espen Benth, Universitetet i Oslo
Leder av disputas
Instituttleder Geir Dahl, Matematisk institutt, Universitet i Oslo
- Professor Nils Henrik Risebro, Matematisk institutt, Universitet i Oslo
- Professor Kenneth Hvistendahl Karlsen, Matematisk institutt, Universitet i Oslo
Numerical methods are of incredible importance in all kinds of physical applications based on solving partial differential equations. In this thesis, I analysed and developed numerical methods for a particular class of partial differential equations called hyperbolic conservation laws which appear in a multitude of models including models in oceanography, gas dynamics, and traffic flow. The numerical methods in question are used in practice to approximate solutions of such models and these solutions can then be used to predict wave heights in ocean currents, the yield of gas flowing through a pipeline, and high density traffic situations for example. On the other hand, numerical methods are a tool to prove theoretical properties of the underlying model which can either justify the model or lead to its rejection.
In particular, the findings of my thesis include techniques to incorporate boundary conditions in finite volume methods for conservation laws with a nonlocal source term arising in modelling ocean waves and novel numerical methods with high accuracy for conservation laws with a nonlocal flux.
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