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On Suppressing Spurious Oscillations in the Numerical Solution of Hyperbolic Conservation Laws

Abstract:

During the numerical solution of a hyperbolic conservation law, signs of nonlinear instability are most often indicated by the presence of numerical artifacts known as spurious oscillations.This thesis discusses some spatial discretization schemes and time integration methods that are designed to reduce the likelihood of spurious oscillations in the numerical solution of a one-dimensional hyperbolic conservation law. The Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory schemes as well as the Monotonic Upstream Centred Scheme for Conservation Laws are considered for the spatial discretization. Strong-Stability-Preserving Runge-Kutta methods are considered for the time evolution. In addition to the results given by these methods, some stability restrictions are considered inluding linear stability step size restrictions, the CFL condition, and the theoretical and practical monotonicity conditions for a class of second-order explicit Runge-Kutta methods.

Author: Joel Patterson

Advisor: Raymond J. Spiteri

Download: jpatterson_msc_thesis