Numerical stabilization with boundary controls for hyperbolic systems of balance laws

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University of Pretoria

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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.

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Dissertation (MSc)--University of Pretoria, 2016.

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Sustainable Development Goals

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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>