Phase-resolved coastal wave modelling using a non-hydrostatic multilayer formulation
Abstract
We present a non-hydrostatic multilayer solver adapted for phase-resolved simulation of coastal wave dynamics over complex bathymetry and in the presence of coastal structures. The solver discretises the incompressible Navier-Stokes equations using a vertically Lagrangian layered representation in which the layer interfaces are material surfaces and a non-hydrostatic pressure correction couples the layers. A relatively small number of layers suffices to represent the smooth vertical structure of surface gravity waves, so the formulation resolves dispersive nonlinear wave dynamics efficiently over a wide range of water depths. A generating-absorbing boundary condition (GABC) based on a dispersive Padé approximation of the linear dispersion relation is implemented, enabling simultaneous wave generation and absorption of reflections at the boundary without extended relaxation zones. An embedded-boundary formulation is introduced that enables the representation of vertical coastal structures such as breakwaters and quay walls within the multilayer framework. The model is validated against laboratory experiments covering linear, nonlinear and breaking wave conditions, wave transformation over variable bathymetry, wave loads on a bottom-mounted cylinder, and diffraction through harbour openings, and is benchmarked against a volume-of-fluid reference solver and the SWASH and FUNWAVE wave models. Numerical energy losses remain below one per cent during long-distance propagation, and the energy dissipation of waves breaking on a beach is reproduced without an empirical breaking closure. The generating-absorbing boundary achieves measured reflection coefficients of a few per cent across the dispersive range, and the embedded boundary reproduces the measured wave loads on a vertical cylinder, including the secondary load cycle.
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BibTeX
@article{lande2026phaseresolved,
title = {{Phase-resolved coastal wave modelling using a non-hydrostatic multilayer formulation}},
author = {Øystein Lande and Stéphane Popinet and Odin Gramstad and Thomas B Johannessen and Atle Jensen},
journal = {Coastal Engineering},
year = {2026},
month = oct,
doi = {10.1016/j.coastaleng.2026.105177},
url = {https://hal.science/hal-05848198v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Phase-resolved coastal wave modelling using a non-hydrostatic multilayer formulation
AU - Øystein Lande
AU - Stéphane Popinet
AU - Odin Gramstad
AU - Thomas B Johannessen
AU - Atle Jensen
PY - 2026
DA - 2026/10/31
JO - Coastal Engineering
DO - 10.1016/j.coastaleng.2026.105177
UR - https://hal.science/hal-05848198v1
AB - We present a non-hydrostatic multilayer solver adapted for phase-resolved simulation of coastal wave dynamics over complex bathymetry and in the presence of coastal structures. The solver discretises the incompressible Navier-Stokes equations using a vertically Lagrangian layered representation in which the layer interfaces are material surfaces and a non-hydrostatic pressure correction couples the layers. A relatively small number of layers suffices to represent the smooth vertical structure of surface gravity waves, so the formulation resolves dispersive nonlinear wave dynamics efficiently over a wide range of water depths. A generating-absorbing boundary condition (GABC) based on a dispersive Padé approximation of the linear dispersion relation is implemented, enabling simultaneous wave generation and absorption of reflections at the boundary without extended relaxation zones. An embedded-boundary formulation is introduced that enables the representation of vertical coastal structures such as breakwaters and quay walls within the multilayer framework. The model is validated against laboratory experiments covering linear, nonlinear and breaking wave conditions, wave transformation over variable bathymetry, wave loads on a bottom-mounted cylinder, and diffraction through harbour openings, and is benchmarked against a volume-of-fluid reference solver and the SWASH and FUNWAVE wave models. Numerical energy losses remain below one per cent during long-distance propagation, and the energy dissipation of waves breaking on a beach is reproduced without an empirical breaking closure. The generating-absorbing boundary achieves measured reflection coefficients of a few per cent across the dispersive range, and the embedded boundary reproduces the measured wave loads on a vertical cylinder, including the secondary load cycle.
SN - 0378-3839
SN - 1872-7379
ER -