Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering & Technology, 7 (3.28) (2018) 97-101 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed Mohammad Fadhli Ahmad*, Mohd Sofiyan Sulaiman School of Ocean Engineering, Universiti Malaysia Terengganu, 21300 Kuala Nerus, Terengganu, Malaysia *Corresponding author E-mail: fadhli@umt.edu.my Abstract 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. Keywords: Numerical schemes, dam break, finite difference method, wave propagation, uneven bottom seabed 1. Introduction Coastal ocean is strongly affected by human interference and cli- mate change issue as portrayed in the past [1]. Understanding of coastal change through numerical modelling is one of the most effective tools. Reconstructions of historic states, hindcasts and analysis of the dynamics in the last decades, short term forecasts of coastal ocean states, as well as for coastal climate projections and possible future scenarios are possible through numerical mod- elling implementation [2]. Initially, the implementations of numer- ical schemes were conducted at the shallow water model without considering the sediment transport and bed level models. Acquir- ing bed sediment size is crucial for sediment transport prediction [3]. Nevertheless, sediment transport study at coastal areas are differ significantly with the stream channel due to bed material size, directional flows and nature of water level fluctuations [4, 5]. Advanced computer technology has opened up the possibility of modelling the hydrodynamics and sediment transport to carry out the engineering appraisal for many coastal engineering works. One-dimensional models of sediment transport in stream have seen extensive development over the past decades. These models have been frequently used to simulate the cohesive sediment transport and morphological changes in river, tidal channels and the salt wedge formation in estuaries [6]. In [7] developed a one- dimensional sediment transport model, in which the standard shal- low water equations were solved for two layers of water depth to provide the flow field. The main aim of this paper is to solve hy- drodynamic equations using finite difference model of Lax- Wndroff scheme and Lax-Friederichs scheme. The ability of these schemes to model wave propagation will be compared with ana- lytical results. In [8] successfully demonstrated the use of finite difference element to simulate three-dimensional shallow water flow. The robustness and correctness of Lax-Wendroff and Lax- Friederichs numerical schemes were put into test by looking at the scenario of dam break problem and wave propagation mechanics. 2. Methodology There are a lot available finite difference schemes in the literature such as artificial dissipation (AD), localized artificial diffusivity (LAD) and weighted essentially non-oscillatory (WENO) schemes. Those are high order schemes as previously described by [9]. The shallow water equations can be solved using the ordinary finite difference methods such as Lax-Friederichs and Lax-Wendroff numerical schemes. The selection of those schemes are based on the stability of Lax-Friederichs and Lax-Wendroff numerical schemes to solve nonlinear problem [10]. The shallow water equa- tions can be written in the conservation form as   +   =  …. (1) where =[  ℎ ],=[ ℎ  2 + 1 2 ℎ 2 ],=[ 0  1 ] in which  is a conservation variable,  is a physical flux and  is the source term. All these terms are written in a vector form. The source term usually consists of the bed slope term, friction term and etc.