Citation: Tarwidi, D.; Pudjaprasetya, S.R.; Tjandra, S.S. A Non-Hydrostatic Model for Simulating Weakly Dispersive Landslide-Generated Waves. Water 2023, 15, 652. https:// doi.org/10.3390/w15040652 Academic Editor: Roberto Greco Received: 28 November 2022 Revised: 12 January 2023 Accepted: 2 February 2023 Published: 7 February 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). water Article A Non-Hydrostatic Model for Simulating Weakly Dispersive Landslide-Generated Waves Dede Tarwidi 1,2, * , Sri Redjeki Pudjaprasetya 1 and Sugih Sudharma Tjandra 3 1 Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha No. 10, Bandung 40132, Indonesia 2 School of Computing, Telkom University, Jalan Telekomunikasi No. 1 Terusan Buah Batu, Bandung 40257, Indonesia 3 Industrial Engineering, Parahyangan Catholic University, Jalan Ciumbuleuit No. 94, Bandung 40141, Indonesia * Correspondence: dedetarwidi@telkomuniversity.ac.id Abstract: The aim of this study is to develop an efficient numerical scheme that is capable of simu- lating landslide-generated waves. The numerical scheme is based on the one-layer non-hydrostatic (NH-1L) model, a phase-solving model that can account for weakly dispersive waves. In this paper, the model is extended to include a time-varying solid bed. This NH-1L scheme is very efficient because, at each time step, only a tridiagonal Poisson pressure matrix needs to be solved. In this study, the capability of the NH-1L scheme to simulate landslide-generated waves is demonstrated by executing two types of landslide motion: constant speed and with acceleration and deceleration. Validation was performed using analytical solutions of the linear weakly dispersive (LWD) model, as well as experimental data. The NH-1L model was capable of describing the generation and propagation of water waves by a submarine landslide from relatively intermediate water to shallow water depths. Keywords: non-hydrostatic model; weakly dispersive wave; submarine landslide; tsunami 1. Introduction Landslide-induced tsunamis are natural disasters that can strike the coast without warning because they may not be preceded by earthquakes. Therefore, it is important to predict the magnitude and initial location of these tsunamis. Although landslide tsunamis account for only 7% of all tsunamis [1], they are nearly as destructive as earthquake- triggered tsunamis. This motivates a comprehensive study of landslide-generated waves that is necessary for the development of disaster mitigation strategies. The application of numerical models may provide solutions to these issues. There have been several attempts to develop numerical models capable of simulating landslide tsunamis. Non-linear shallow water equations are commonly used due to their simplicity and efficiency in tsunami modeling [2–6]. However, these models are less accurate when simulating the generation of tsunamis in areas of intermediate or deep water depth, where the dispersion effects are fairly significant. Other models that integrate non-linear and dispersion effects are Boussinesq-type wave equations [7–11] and potential flow equations [12–14]. However, numerical approaches to Boussinesq-type models are difficult to implement due to the presence of mixed high-order derivative variables, while the application of potential flow models is restricted by the assumption of ideal fluids and irrotational motion [15]. Moreover, the other widely used dispersive models for landslide- generated tsunamis are based on the Navier–Stokes equations [16–20]. Unfortunately, due to their computational complexity, these models are costly to calculate. The non-hydrostatic model is a wave model derived from the Navier–Stokes equations with hydrodynamic pressure along the flow depth [21–25]. The efficiency and accuracy of Water 2023, 15, 652. https://doi.org/10.3390/w15040652 https://www.mdpi.com/journal/water