Semi-Lagrangian numerical simulation method for tides in coastal regions
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ORIGINAL ARTICLE
Semi‑Lagrangian numerical simulation method for tides in coastal regions Yoshiki Nishi1 · Eiki Taniguchi1 · Lisa Niikura1 · Eitetsu Shibata1 Received: 1 June 2019 / Accepted: 17 August 2019 © The Japan Society of Naval Architects and Ocean Engineers (JASNAOE) 2019
Abstract In this paper, a numerical computation method is proposed to simulate tides in coastal regions. The proposed method is based on the hyperbolic form of governing equations and employs a semi-Lagrangian scheme to ensure the accuracy and stability of numerical computations. Open and wall boundary conditions can be treated universally by combining them with the semi-Lagrangian scheme. Furthermore, the method is applied to some benchmark problems of shallow water to examine its performances in wave propagation, wave transparency through open boundaries, and tides in semi-enclosed bays. The results obtained demonstrate that the proposed method can be utilized as a practical tool to investigate tidal dynamics in coastal regions. Keywords Tides · Semi-Lagrangian · Open boundary condition · Wall boundary condition · Coastal region
1 Introduction Computer simulation of tides and tidal currents in coastal seas is a research topic of great interest due to its critical role in predicting the fate of pollutants in seawater and evaluating the potential power of an ocean current. Several numerical computation codes have been constructed to numerically simulate the tides, tidal current, and thermohaline fields. For example, the Princeton Ocean Model (POM) [1] and finite-volume, primitive equation Community Ocean Model (FVCOM) [2] have been widely used by several researchers of physical oceanography and coastal ocean environment because of their ease of usage and excellent performances in theoretical investigations. However, the numerical ocean model needs to eventually become a practical tool that could be employed in environmental impact assessment against ocean-space utilization and evaluation of environmental risk due to marine pollutants. Therefore, there is a need for continuous efforts to refine the model to realize more stable, accurate, and * Yoshiki Nishi nishi‑yoshiki‑[email protected] 1
Department of Systems Design for Ocean‑Space, Faculty of Engineering, Yokohama National University, 79‑5 Tokiwadai, Hodogaya, Yokohama, Kanagawa 2408501, Japan
efficient computations. This study aims to provide a fundamental approach to improve numerical ocean model practicality by implementing a new scheme and algorithm. When predicting the fate of marine pollutants using the ocean model, the tide is one of the most critical factors among a variety of phenomena occurring in the coastal sea; therefore, this study focuses on it primarily. Ocean models developed by earlier studies on tidal simulation can be roughly categorized into the following three groups. The first group refers to models that handle only the external mode of the equations governing the ocean dynamics; whereas the second group includes models that treat the external and internal mo
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