Numerical solution of regularised long ocean waves using periodised scaling functions

In this paper, a numerical technique for solving the regularised long wave equation (RLW) is presented using a wavelet Galerkin (WG) method in space and a fourth-order Runge–Kutta (RK) technique in time. We study the convergence analysis of the obtained numerical solutions and investigate the result...

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Bibliographic Details
Published in:Pramāṇa 2019-05, Vol.92 (5), p.1-15, Article 71
Main Authors: Bakhoday-Paskyabi, M, Valinejad, A, Azodi, H Deilami
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Computer simulation
Energy conservation
Galerkin method
Numerical methods
Observations and Techniques
Ocean waves
Physics
Physics and Astronomy
Runge-Kutta method
Solitary waves
Wave equations
Wavelet analysis
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Summary:In this paper, a numerical technique for solving the regularised long wave equation (RLW) is presented using a wavelet Galerkin (WG) method in space and a fourth-order Runge–Kutta (RK) technique in time. We study the convergence analysis of the obtained numerical solutions and investigate the results for the motions of double and single solitary waves, undular bores and conservation properties of mass, energy and momentum in order to verify the applicability and performance of the proposed method. Simulation results are further compared with the known analytical solutions and some previous published numerical results. It is concluded that the present method remarkably improves the accuracy of the Galerkin-based methods for numerically solving a large class of nonlinear and weakly dispersive ocean waves.
ISSN:0304-4289
0973-7111
DOI:10.1007/s12043-019-1726-2