Title: Investigating the shock-capturing properties of some composite numerical schemes for the 1-D linear advection equation
Authors: Appanah Rao Appadu
Addresses: Centre for Research in Computational and Applied Mechanics, University of Cape Town, 7701 Rondebosch, South Africa
Abstract: This paper enables us to understand better the shock-capturing property of composite schemes. The study allows us to understand why not all composite schemes can be effective to control dispersion and dissipation in regions of shocks when used to solve 1-D linear advection problems. We use a technique called the Minimised Integrated Exponential Error for Low Dispersion and Low Dissipation to analyse the shock-capturing property of some selected numerical methods applied to the 1-D linear advection equation. This technique also allows us to obtain the optimal cfl number. Numerical experiments are performed and the errors are quantified into dispersion and dissipation using a technique devised by Takacs. It is seen that the errors are dependent on the cfl number used. At the optimal cfl, we observe that the dispersion and dissipation errors are least as compared to other cfl numbers.
Keywords: KdVB equation; minimised integrated exponential error; low dispersion; low dissipation; shock capture; composite schemes; linear advection.
International Journal of Computer Applications in Technology, 2012 Vol.43 No.2, pp.79 - 92
Received: 08 May 2021
Accepted: 12 May 2021
Published online: 24 Mar 2012 *