(v1.11) pkg> add WaterWaves1D
using WaterWaves1DWaterWaves1D.jl is a Julia package providing a framework to study and compare several models for the propagation of unidimensional surface gravity waves (a.k.a. "water waves").
Several models are already implemented, including (but not limited to) the so-called water waves system, its truncated spectral expansion, the Green-Naghdi system, the Matsuno system, and so on. You may easily add your favorite one to the gang: see the how-to guide.
See here.
A simple example of a typical use of the package can be found below. More advanced examples are available at the examples and notebooks folders.
Gather parameters of the problem.
param = (
# Physical parameters. Variables are non-dimensionalized as in Lannes, The water waves problem, isbn:978-0-8218-9470-5
μ = 1, # shallow-water dimensionless parameter
ϵ = 1/4, # nonlinearity dimensionless parameter
# Numerical parameters
N = 2^11, # number of collocation points
L = 10, # half-length of the numerical tank (-L,L)
T = 5, # final time of computation
dt = 0.01, # timestep
);Define initial data (here, a "heap of water").
z(x) = exp.(-abs.(x).^4); # surface deformation
v(x) = 0*exp.(-x.^2); # zero initial velocity
init = Init(z,v); # generate the initial data with correct typeSet up initial-value problems for different models to compare.
# Build models
model_WW=WaterWaves(param,verbose=false) # The water waves system
model_WW2=WWn(param;n=2,dealias=1,δ=1/10) # The quadratic model (WW2)
# Build problems
problem_WW=Problem(model_WW, init, param) ;
problem_WW2=Problem(model_WW2, init, param) ;Integrate in time the initial-value problems.
solve!([problem_WW problem_WW2]);Plot solutions at final time.
using Plots
plot([problem_WW, problem_WW2])
Generate an animation.
anim = @animate for t = LinRange(0,5,101)
plot([problem_WW, problem_WW2];T=t,ylims=(-0.5,1))
end
gif(anim, "Example.gif", fps=15)
WaterWaves1D.jl is being developed by Vincent Duchêne and Pierre Navaro.
The code is citable via zenodo. Please cite as:
V. Duchêne, P. Navaro. WaterWaves1D.jl (Version v0.1.0). Zenodo. https://doi.org/10.5281/zenodo.7142921
These preprints and publications use WaterWaves1D.jl.
- Vincent Duchêne and Christian Klein, Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart, Discrete Contin. Dyn. Syst. Ser. B, 27(10), pp. 5905–5933 (2022). DOI: 10.3934/dcdsb.2021300
- Vincent Duchêne and Benjamin Melinand, Rectification of a deep water model for surface gravity waves, Pure Appl. Anal. 6, No. 1, pp. 73–128 (2024). DOI: 10.2140/paa.2024.6.73
- Arnaud Debussche, Etienne Mémin, and Antoine Moneyron, Derivation of Stochastic Models for Coastal Waves, in B. Chapron et al. (eds.), Stochastic Transport in Upper Ocean Dynamics III, Mathematics of Planet Earth 13 (2025). DOI:10.1007/978-3-031-70660-8_9
- Duchêne, Vincent; Marstrander, Johanna Ulvedal, The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems, Preprint, arXiv:2507.00516 (2025). DOI: 10.48550/arXiv.2507.00516
If you have a work that belongs to tis list, please open a pull request to add it or let us know!
If you would like to contribute to the development of the package, please do not refrain from contacting us, for instance by opening an issue.
If this package does not fit your needs, you may consider
SpectralWaves.jlImplementation of a spectral method for water waves over topography.GeophysicalFlows.jlGeophysical fluid dynamics leveraging the pseudo-spectral solver modules of the packageFourierFlows.jl.DispersiveShallowWater.jlStructure-preserving numerical methods for dispersive shallow water models.TrixiShallowWater.jlsimulations of the shallow water equations with the discontinuous Galerkin method.Oceananigans.jlFinite volume simulations of the nonhydrostatic and hydrostatic Boussinesq equations on CPUs and GPUs.