Original scientific paper
A numerical study of SSP time integration methods for hyperbolic conservation laws
Nelida Črnjarić-Žic
; Faculty of Engineering, University of Rijeka, Rijeka, Croatia
Bojan Crnković
; Faculty of Engineering, University of Rijeka, Rijeka, Croatia
Senka Maćešić
; Faculty of Engineering, University of Rijeka, Rijeka, Croatia
Abstract
he method of lines approach for solving hyperbolic conservation laws is based on the idea
of splitting the discretization process in two stages. First, the spatial discretization is performed by
leaving the system continuous in time. This approximation is usually developed in a non-oscillatory
manner with a satisfactory spatial accuracy. The obtained semi-discrete system of ordinary differential
equations (ODE) is then solved by using some standard time integration method.
In the last few years, a series of papers appeared, dealing with the high order strong stability preserving
(SSP) time integration methods that maintain the total variation diminishing (TVD) property of the first
order forward Euler method. In this work the optimal SSP Runge--Kutta methods of different order are
considered in combination with the finite volume weighted essentially non-oscillatory (WENO) discretization.
Furthermore, a new semi--implicit WENO scheme is presented and its properties in combination with different
optimal implicit SSP Runge--Kutta methods are studied. Analysis is made on linear and nonlinear scalar
equations and on Euler equations for gas dynamics.
Keywords
WENO schemes; implicit schemes; hyperbolic conservation law; strong stability property; Runge--Kutta methods
Hrčak ID:
61882
URI
Publication date:
8.12.2010.
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