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This software provides tools for partial differential equations on periodic domains using Fourier-based pseudospectral methods. A central intent of the software's design is also to provide a framework for writing new, fast solvers for new physical problems. The code is written in Julia.

For more details refer to the documentation.


To install, use Julia's built-in package manager to add the package and also to instantiate/build all the required dependencies

julia> using Pkg
julia> Pkg.add("FourierFlows")
julia> Pkg.instantiate()

The most recent version of FourierFlows.jl requires Julia v1.6 (the current long-term-release) or later.

Last version that works with Julia v1.5 is FourierFlows.jl v0.7.2.


See the documentation for tutorials on (i) how construct grids and use Fourier transform to compute derivatives and (ii) how to set up a PDE, time-step it forward, and visualize the output, (iii) how to add diagnostics, and (iv) how to write and read output from disk.


For now, FourierFlows.jl is restricted to run on either a single CPU or single GPU. Multi-threading can enhance performance for the Fourier transforms. By default, FourierFlows.jl will use the maximum number of threads available on your machine. You can set the number of threads used by FourierFlows.jl by setting the environment variable, e.g.,


For more information on multi-threading users are directed to the Julia Documentation.

If your machine has more than one GPU available, then functionality within CUDA.jl package enables the user to choose the GPU device that FourierFlows.jl should use. The user is referred to the CUDA.jl Documentation; in particular, CUDA.devices and CUDA.CuDevice.


A demonstration for how to code up and solve the linear shallow water equations is found in the Examples section of the documentation.

For more examples of FourierFlows.jl in action, see the child packages GeophysicalFlows.jl or PassiveTracerFlows.jl.

Getting help

Interested in using FourierFlows.jl or trying to figure out how to use it? Please feel free to ask us questions and get in touch! The documentation is always the best place to start. Check out the examples and open an issue or start a discussion if you have any questions, comments, suggestions, etc.


FourierFlows.jl started during the on Atmospheric and Oceanic Fluid Dynamics Meeting 2017 by Greg Wagner and Navid Constantinou. Since then various people have contributed.


This software is citable via zenodo. Please cite as:

Gregory L. Wagner, Navid C. Constantinou, and contributors. (2023). FourierFlows/FourierFlows.jl: FourierFlows v0.10.3 (Version v0.10.3). Zenodo.


We are excited to get more people involved in contributing to the development of FourierFlows.jl! We welcome any contribution, no matter how big or small! It's always great to have new people look at the code with fresh eyes: you will see errors that other developers have missed.

Let us know by open an issue or start a discussion if you'd like to work on a new feature or implement a new module, if you're new to open-source and want to find a cool little project or issue to work on that fits your interests! We're more than happy to help along the way.

For more information, check out our contributor's guide.