Flower1D.jl

Flux reconstruction fluid flow solver in Julia.

Overview

Flower1D.jl is a pure Julia implementation of a flux reconstruction (high-order) solver of 1D PDEs: Linear advection, Burgers, viscous Burgers, and Euler equations. Currently, it is used for educational and academic purposes, but future developments will be focused in 2D and 3D versions for unstructured grids.

Numerical methods

The mesh can be arbitrarily discretized into N elements, and each element is represented with Lagrange polynomials of degree P, hence using P + 1 solution points within each element. Furthermore, a continuos flux is obtained with VCJH correction schemes, governed by the C parameter, which can recover different high-order formulations. The solution points within each element can follow an "equidistant" distribution or a "legendre" distribution. The time-integration methods available are Euler (1st order) and Runge-Kutta (2nd and 3rd order).

Installation, usage, and development

To install the package (plus dependencies) use

julia
(v1.x) pkg> add "git@github.com:b-fg/Flower1D.jl.git"

You can now download the examples and run them by previously loading the package

using Flower1D

If you wish to download the source code and play with it: clone the repo, install the package, and mark it for local development

git clone git@github.com:b-fg/Flower1D.jl
cd Flower1D.jl
julia
(v1.x) pkg> add .
(v1.x) pkg> dev --local Flower1D

Now you can run any example using

cd Flower1D.jl
julia --project
julia > include("examples/burgers_advection_diffusion/main.jl")

Modifications in the source code will be re-compiled with Revise.jl.

Note that examples for all the available PDEs and flux reconstruction functionalities can be found in examples/. Documentation will soon be available in docs/.

Contributions and future work

Contributions are most welcomed! Please submit a pull request and we will work together to include your changes in the package 😄.

Future features development will be related to:

Extension to structured 2D and 3D geometries.
Extension to unstructured grids.
Artificial viscosity for stabilisation.
Compressible Navier-Stokes equations.
Parallel computing using Distributed.jl.
Adaptive h/p refinement.
VTK input/output.

Cite the repo!

If you find this repository useful, please cite it:

@misc{Flower1D.jl,
  author = {B. Font},
  title = {Flower1D.jl: Flux reconstruction fluid flow solver for 1D {PDE}s},
  year = {2022},
  publisher = {GitHub},
  journal = {GitHub repository},
  url = {https://github.com/b-fg/Flower1D.jl},
}

b-fg / Flower1D.jl