WaterWaves1D.jl
Installation
(v1.8) pkg> add WaterWaves1D
using WaterWaves1DOverview
WaterWaves1D.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.
Documentation
See here.
Example
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)
Developers
WaterWaves1D.jl is being developed by Vincent Duchêne and Pierre Navaro.
Citing
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