Numerical study of nonlinear wave processes by means of discrete chain models

Obregon, M. and Raj, N. and Stepanyants, Y. ORCID: https://orcid.org/0000-0003-4546-0310 (2012) Numerical study of nonlinear wave processes by means of discrete chain models. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

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Abstract

We show that many nonlinear wave processes in dispersive and dissipative media can be numerically studied by means of chain models describable by sets of ODEs. This allows us to obtain higher accuracy results for relatively cheap price using standard ODE-solvers. The advantages of this approach in comparison with the direct numerical modeling of PDEs are: (i) the chain model has a vivid physical meaning and can be created in a laboratory in various embodiments playing a role of analogous computers; (ii) there is no need to develop a complex numerical scheme and study its stability and convergence. We demonstrate the idea in application to the modeling of solitary wave propagation in a rotating ocean described by the Gardner–Ostrovsky PDE using a modified Toda chain model. We show that our results are in a good agreement with approximate theoretical findings and early published data obtained from the direct numerical modeling of the Gardner–Ostrovsky PDE.

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Item Type:	Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	No evidence of copyright restrictions preventing deposit.
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited:	15 Apr 2013 23:30
Last Modified:	15 Feb 2021 23:33
Uncontrolled Keywords:	nonlinear waves; numerical modeling; Soliton; Ostrovsky equation; Toda chain
Fields of Research (2008):	01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations 09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations 40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/23150

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