Staggered Numerical Modeling for Investigating the Effectiveness of Embankment and Vegetation on the Reduction of Wave Run-up Iryanto 1 , Muhamad Mustamiin 2 , Munengsih Sari Bunga 3 , Ikha Magdalena 4 , and Novry Erwina 5 {iryanto.math@yahoo.com 1 , m.mustamiin@gmail.com 2 , nengslim85@gmail.com 3 } Informatics Department, Politeknik Negeri Indramayu, Indonesia 1 , Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia 2 Abstract. In this research, we develop a mathematical model to investigate the effectiveness of embankment and vegetation on the reduction of wave run-up. We solve the model numerically using a staggered conservative scheme. Wave run-up testing on a sloping beach is conducted to show the accuracy of our numerical scheme. In this case, we compare our numerical results with data of laboratory experiments of Synolakis provided in [9]. The results of the comparison show that the numerical results are in good agreement with the experimental data. Further, the results of the influence of the vegetation, embankment, and combination of both of them are presented in the article. Keywords: Staggered numerical modeling, staggered conservative scheme, embankment, vegetation, wave run-up, shallow water model 1 Introduction Sea wave has potential to threat (even to destroy) coastal area. Some examples of the phenomena are tsunami and abrasion. In order to minimize the destruction of the area, some methods are used such as by planting vegetation or by building embankment as a wave barrier. This article is focused on numerical modeling for investigating the effectiveness of embankment and vegetation on the reduction wave run-up. Numerical modeling on each case (embankment or vegetation only) can be found in many references for instances see [1], [2] for the vegetation modeling and [3], [4] for the embankment modelling. In the work of Adytia et al. in [1], the model is based on shallow water equations with Manning friction. The model was solved numerically using staggered conservative scheme. Further, the shallow water model was also used to describe overtopping over sea dike as described in [4]. Wave interaction with vegetation can be modelled also using Navier-Stokes type equations as described in [2]. In the reference, influence of vegetation is considered as friction. Several frictions such as Manning, Darcy, and laminar, were used in the reference to model the influence of vegetation. Wave run up is also often observed in the problem. An accurate run up prediction becomes important thing in the reseacrh field and several authors focused their research in the area for instances see [5], [6], [7], and [8]. Different model and numerical method are used to solve the problem. In the field of wave run up, data of laboratory experiment of Synolakis as described in MSCEIS 2019, October 12, Bandung, Indonesia Copyright © 2020 EAI DOI 10.4108/eai.12-10-2019.2296420