Numerical stabilization with boundary controls for hyperbolic systems of balance laws
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Pretoria
Abstract
In this dissertation, boundary stabilization of a linear hyperbolic system of balance laws is
considered. Of particular interest is the numerical boundary stabilization of such systems. An
analytical stability analysis of the system will be presented as a preamble. A discussion of
the application of the analysis on speci c examples: telegrapher equations, isentropic Euler
equations, Saint-Venant equations and Saint-Venant-Exner equations is also presented. The
rst order explicit upwind scheme is applied for the spatial discretization. For the temporal
discretization a splitting technique is applied. A discrete ²−Lyapunov function is employed
to investigate conditions for the stability of the system. A numerical analysis is undertaken and
convergence of the solution to its equilibrium is proved. Further a numerical implementation
is presented. The numerical computations also demonstrate the stability of the numerical
scheme with parameters chosen to satisfy the stability requirements.
Description
Dissertation (MSc)--University of Pretoria, 2016.
Keywords
UCTD
Sustainable Development Goals
Citation
Weldegiyorgis, GY 2016, Numerical stabilization with boundary controls for hyperbolic systems of balance laws, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/60870>