Open AccessDeficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed
Author(s) -
Mohammad Fadhli Ahmad,
Mohd Sofiyan Suliman
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i3.28.20977
Subject(s) - classification of discontinuities , seabed , dissipation , oscillation (cell signaling) , finite difference , finite difference method , shock wave , wave propagation , free surface , mechanics , shallow water equations , geology , waves and shallow water , geotechnical engineering , mathematical analysis , mathematics , physics , oceanography , genetics , quantum mechanics , biology , thermodynamics
The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce non-oscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.