Preprint 2026-14
Raimund Bürger, Cipriano Escalante, Enrique D. Fernández Nieto, Jorge Moya:
A two-dimensional multilayer shallow water model of tsunami-forest interaction
Abstract:
Investigating the interaction of tsunamis with coastal forests is essential for assessing the protective role of coastal vegetation. This interaction can be described by a multilayer shallow-water model in two horizontal space dimensions, which is derived from a free-surface formulation of the Euler equations for an ideal fluid. The resulting governing equations are approximated by a layer-averaged non-hydrostatic (LDNH) approach. Within the LDNH framework pressures are treated as linear functions within each layer and velocities are represented as piecewise constant. Following [K. Iimura, N. Tanaka, Numerical simulation estimating effects of tree density distribution in coastal forest on tsunami mitigation, Ocean Engrg. 54 (20212) 223–232], additional source terms describing drag, inertia, and porosity effects are incorporated to represent momentum exchange between the flow and the forested terrain. These factors are specified in each vertical layer to achieve a more detailed description of vegetation structure than is possible with single-layer formulations. The resulting horizontally two-dimensional multilayer system is approximated numerically by combining projection techniques for the non-hydrostatic pressure with polynomial viscosity finite volume schemes of the PVM class [M. J. Castro, E. D. Fernández-Nieto, A class of computationally fast first order finite volume solvers: PVM methods, SIAM J. Sci. Comput. 34 (2012) A2173–A2196]. This methodology allows efficient simulation of tsunami propagation and onshore inundation in the presence of vegetated landscapes. The model performance and numerical method are assessed through comparisons with laboratory measurements and available observational data. In general good agreement is obtained. The simulations further support the conclusion that coastal vegetation can provide substantial attenuation of tsunami impact and thus serves as a valuable component of natural coastal defense strategies.
