Proceedings of the International Conference on Applied Sciences and Engineering (ICASE 2023)

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Generalized integral representation method as applied to numerical simulation of Boussinesq wave

Authors
Gantulga Tsedendorj1, Baljinnyam Tsangia2, Khongorzul Dorjgotov3, *
1Department of Mathematics, School of Arts and Sciences, National University of Mongolia, Ulaanbaatar, Mongolia
2Department of Mathematics, School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia
3Department of Applied Mathematics, School of Engineering and Applied Sciences, National University of Mongolia, Ulaanbaatar, Mongolia
*Corresponding author. Email: khongorzul@seas.num.edu.mn
Corresponding Author
Khongorzul Dorjgotov
Available Online 31 December 2023.
DOI
10.2991/978-94-6463-330-6_4How to use a DOI?
Keywords
Numerical Simulation of Boussinesq Wave; Soliton Interactions; Generalized Integral Representation Method (GIRM); Numerical Schemes based on GIRM
Abstract

In this study, we present discretization schemes based on Generalized Integral Representation Method (GIRM) for numerical simulation of the Boussinesq wave. The schemes numerically evaluate the coupled Boussinesq equation for different solitary wave phenomena, namely, propagation of a single soliton, head-on collision of two solitons and reflection of a soliton at a fixed wall boundary. In these three soliton interactions, we utilize different Generalized Fundamental Solutions (GFS) along with piecewise constant approximations for the unknown functions. For the case of soliton reflection at a wall, time evolution in GIRM is coupled with the Green’s function in order to cope with the complicated boundary conditions that arise from the GIRM derivation. We conduct numerical experiments and obtain satisfactory approximate result for each case of the soliton interactions.

Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the International Conference on Applied Sciences and Engineering (ICASE 2023)
Series
Atlantis Highlights in Engineering
Publication Date
31 December 2023
ISBN
978-94-6463-330-6
ISSN
2589-4943
DOI
10.2991/978-94-6463-330-6_4How to use a DOI?
Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Gantulga Tsedendorj
AU  - Baljinnyam Tsangia
AU  - Khongorzul Dorjgotov
PY  - 2023
DA  - 2023/12/31
TI  - Generalized integral representation method as applied to numerical simulation of Boussinesq wave
BT  - Proceedings of the International Conference on Applied Sciences and Engineering (ICASE 2023)
PB  - Atlantis Press
SP  - 24
EP  - 30
SN  - 2589-4943
UR  - https://doi.org/10.2991/978-94-6463-330-6_4
DO  - 10.2991/978-94-6463-330-6_4
ID  - Tsedendorj2023
ER  -