A multilayer shallow water model for tsunamis and coastal forest interaction

¹ CI 2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
² Departamento de Matemática Aplicada I, ETS Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes No. 2, 41012 Sevilla, Spain

^* Corresponding author: jorgemoya@udec.cl; jmoya1@us.es

Received: 7 May 2024
Accepted: 7 March 2025

Abstract

Models and numerical methods of the impact of tsunamis on coastal forests are of vital importance for exploring the potential of coastal vegetation as a means of mitigation. Such a model is formulated as a multilayer shallow water system based on a free-surface formulation of the Euler equations for an ideal fluid. Specifically, the Euler equations are approximated by a layer averaged non-hydrostatic (LDNH) approach involving linear pressures and piecewise constant velocities. Furthermore, based on [Iimura and Tanaka, Ocean Eng. 54 (2012) 223–232] drag forces, inertia forces, and porosity are added to model the interaction with the forest. These ingredients are specified in a layer-wise manner. Thus, the vertical features of the forest are described with higher accuracy than within a single-layer approach. Projection methods for the non-hydrostatic pressure in conjunction with polynomial viscosity matrix finite volume methods [Castro and Fernández-Nieto, SIAM J. Sci. Comput. 34 (2012) A2173–A2196] are employed for the numerical solution of the multilayer model, that is for the propagation of tsunamis and coastal flooding. Experimental observations and field data are used to validate the model. In general good agreement is obtained.