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Comparison of Numerical Diffusion of Mass Transport in Shock Capturing Methods for a Density Coupled Shallow Water Model

Author(s): Alberto De La Fuente; P. Andrew Sleigh; Yarko Nino

Linked Author(s): Alberto de la Fuente, Andrew Sleigh, Yarko Niño

Keywords: Numerical models; Saline transport scheme; Riemann solver; Shock capturing

Abstract: Numerical diffusion and unphysical behaviour was detected during the treatment of transport equations solved with a number of Riemann solver based shock capturing schemes. In this paper an alternative method is presented and discussed which is shown to resolve some of the problems encountered with the other methods. A comparison between different solution schemes for the transport equations is presented. Analysis is presented based upon a novel methodology which allows the quantification of the numerical diffusion in a scheme. This is achieved by numerically fitting a diffusion coefficient to the analytic solution for the advection/diffusion front in a rectangular channel. Finally, a series of test were performed in order to show different aspects relating to the accuracy of the presented advection scheme, such as symmetry of solution, mass conservation, and peak attenuation for “triangle” and “top hat” source shapes advected along a channel.


Year: 2007

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