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A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations

Shiach, Jon B. and Mingham, Clive G. (2008) A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations. ISSN 0378-3839

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Abstract

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.

Item Type: Article
Additional Information: Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in Coastal engineering, published by and copyright Elsevier.
Divisions: Faculties > Faculty of Science and Engineering > Department of Computing, Mathematics & Digital Technology
Faculties > Faculty of Science and Engineering > Department of Computing and Mathematics: Centre for Mathematical Modelling and Flow Analysis (CMMFA)
Date Deposited: 13 Aug 2008 08:44
Last Modified: 01 Sep 2016 13:54
URI: http://e-space.mmu.ac.uk/id/eprint/35232

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