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https://github.com/trixi-framework/Trixi.jl

Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia
https://github.com/trixi-framework/Trixi.jl

adaptive-mesh-refinement amr conservation-laws discontinuous-galerkin hyperbolic-equations julia numerical-simulation-framework simulation summation-by-parts

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Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia

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README 

        
# Trixi.jl



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***

**Trixi.jl at JuliaCon 2024**


At this year's JuliaCon in Eindhoven, Netherlands, we will be present with several contributions

from the Trixi Framework ecosystem:



* [**Julia for Particle-Based Multiphysics with TrixiParticles.jl**](https://pretalx.com/juliacon2024/talk/TPFF8L/),


  [*Erik Faulhaber*](https://github.com/efaulhaber/), [*Niklas Neher*](https://github.com/lasnikas/),

  10th July 2024, 11:00–11:30, Function (4.1)

* [**Towards Aerodynamic Simulations in Julia with Trixi.jl**](https://pretalx.com/juliacon2024/talk/XH8KBG/),


  [*Daniel Doehring*](https://github.com/danieldoehring/),

  10th July 2024, 15:30–16:00, While Loop (4.2)

* [**libtrixi: serving legacy codes in earth system modeling with fresh Julia CFD**](https://pretalx.com/juliacon2024/talk/SXC7LA/),


  [*Benedict Geihe*](https://github.com/benegee/),

  12th July 2024, 14:00–17:00, Function (4.1)



The last talk is part of the 

[Julia for High-Performance Computing](https://juliacon.org/2024/minisymposia/hpc/)

minisymposium, which this year is hosted by our own [*Hendrik Ranocha*](https://github.com/ranocha/).



We are looking forward to seeing you there ♥️

***



**Trixi.jl** is a numerical simulation framework for conservation

laws written in [Julia](https://julialang.org). A key objective for the

framework is to be useful to both scientists and students. Therefore, next to

having an extensible design with a fast implementation, Trixi.jl is

focused on being easy to use for new or inexperienced users, including the

installation and postprocessing procedures. Its features include:



* 1D, 2D, and 3D simulations on [line/quad/hex/simplex meshes](https://trixi-framework.github.io/Trixi.jl/stable/overview/#Semidiscretizations)

  * Cartesian and curvilinear meshes

  * Conforming and non-conforming meshes

  * Structured and unstructured meshes

  * Hierarchical quadtree/octree grid with adaptive mesh refinement

  * Forests of quadtrees/octrees with [p4est](https://github.com/cburstedde/p4est) via [P4est.jl](https://github.com/trixi-framework/P4est.jl)

* High-order accuracy in space and time

* Discontinuous Galerkin methods

  * Kinetic energy-preserving and entropy-stable methods based on flux differencing

  * Entropy-stable shock capturing

  * Positivity-preserving limiting

  * [Finite difference summation by parts (SBP) methods](https://github.com/ranocha/SummationByPartsOperators.jl)

* Compatible with the [SciML ecosystem for ordinary differential equations](https://diffeq.sciml.ai/latest/)

  * [Explicit low-storage Runge-Kutta time integration](https://diffeq.sciml.ai/latest/solvers/ode_solve/#Low-Storage-Methods)

  * [Strong stability preserving methods](https://diffeq.sciml.ai/latest/solvers/ode_solve/#Explicit-Strong-Stability-Preserving-Runge-Kutta-Methods-for-Hyperbolic-PDEs-(Conservation-Laws))

  * CFL-based and error-based time step control

* Native support for differentiable programming

  * Forward mode automatic differentiation via [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl)

* Periodic and weakly-enforced boundary conditions

* Multiple governing equations:

  * Compressible Euler equations

  * Compressible Navier-Stokes equations

  * Magnetohydrodynamics (MHD) equations

  * Multi-component compressible Euler and MHD equations

  * Linearized Euler and acoustic perturbation equations

  * Hyperbolic diffusion equations for elliptic problems

  * Lattice-Boltzmann equations (D2Q9 and D3Q27 schemes)

  * Shallow water equations

  * Several scalar conservation laws (e.g., linear advection, Burgers' equation, LWR traffic flow)

* Multi-physics simulations

  * [Self-gravitating gas dynamics](https://github.com/trixi-framework/paper-self-gravitating-gas-dynamics)

* Shared-memory parallelization via multithreading

* Multi-node parallelization via MPI

* Visualization and postprocessing of the results

  * In-situ and a posteriori visualization with [Plots.jl](https://github.com/JuliaPlots/Plots.jl)

  * Interactive visualization with [Makie.jl](https://makie.juliaplots.org/)

  * Postprocessing with ParaView/VisIt via [Trixi2Vtk](https://github.com/trixi-framework/Trixi2Vtk.jl)



## Installation

If you have not yet installed Julia, please [follow the instructions for your

operating system](https://julialang.org/downloads/platform/). Trixi.jl works

with Julia v1.8 and newer. We recommend using the latest stable release of Julia.



### For users

Trixi.jl and its related tools are registered Julia packages. Hence, you

can install Trixi.jl, the visualization tool

[Trixi2Vtk](https://github.com/trixi-framework/Trixi2Vtk.jl),

[OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl), and

[Plots.jl](https://github.com/JuliaPlots/Plots.jl)

by executing the following commands in the Julia REPL:

```julia

julia> using Pkg



julia> Pkg.add(["Trixi", "Trixi2Vtk", "OrdinaryDiffEq", "Plots"])

```

You can copy and paste all commands to the REPL *including* the leading

`julia>` prompts - they will automatically be stripped away by Julia.

The package [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl)

provides time integration schemes used by Trixi.jl, while

[Plots.jl](https://github.com/JuliaPlots/Plots.jl) can be used to directly

visualize Trixi.jl's results from the REPL.



*Note on package versions:* If some of the examples for how to use Trixi.jl do not

work, verify that you are using a recent Trixi.jl release by comparing the

installed Trixi.jl version from

```julia

julia> using Pkg; Pkg.update("Trixi"); Pkg.status("Trixi")

```

to the [latest release](https://github.com/trixi-framework/Trixi.jl/releases/latest).

If the installed version does not match the current release, please check the

*Troubleshooting* section in the [documentation](#documentation).



The commands above can also be used to update Trixi.jl. A brief list of notable

changes to Trixi.jl is available in [`NEWS.md`](NEWS.md).



### For developers

If you plan on editing Trixi.jl itself, you can download Trixi.jl locally and use the

code from the cloned directory:

```bash

git clone [email protected]:trixi-framework/Trixi.jl.git

cd Trixi.jl

mkdir run

cd run

julia --project=. -e 'using Pkg; Pkg.develop(PackageSpec(path=".."))' # Install local Trixi.jl clone

julia --project=. -e 'using Pkg; Pkg.add(["OrdinaryDiffEq", "Trixi2Vtk", "Plots"])' # Install additional packages

```

Note that the postprocessing tools Trixi2Vtk.jl and Plots.jl are optional and

can be omitted.



If you installed Trixi.jl this way, you always have to start Julia with the `--project`

flag set to your `run` directory, e.g.,

```bash

julia --project=.

```

if already inside the `run` directory.

Further details can be found in the [documentation](#documentation).



## Usage

In the Julia REPL, first load the package Trixi.jl

```julia

julia> using Trixi

```

Then start a simulation by executing

```julia

julia> trixi_include(default_example())

```

Please be patient since Julia will compile the code just before running it.

To visualize the results, load the package Plots

```julia

julia> using Plots

```

and generate a heatmap plot of the results with

```julia

julia> plot(sol) # No trailing semicolon, otherwise no plot is shown

```

This will open a new window with a 2D visualization of the final solution:



  




The method `trixi_include(...)` expects a single string argument with the path to a

Trixi.jl elixir, i.e., a text file containing Julia code necessary to set up and run a

simulation. To quickly see Trixi.jl in action, `default_example()`

returns the path to an example elixir with a short, two-dimensional

problem setup. A list of all example elixirs packaged with Trixi.jl can be

obtained by running `get_examples()`. Alternatively, you can also browse the

[`examples/`](examples/) subdirectory.

If you want to modify one of the elixirs to set up your own simulation,

download it to your machine, edit the configuration, and pass the file path to

`trixi_include(...)`.



*Note on performance:* Julia uses just-in-time compilation to transform its

source code to native, optimized machine code at the *time of execution* and

caches the compiled methods for further use. That means that the first execution

of a Julia method is typically slow, with subsequent runs being much faster. For

instance, in the example above the first execution of `trixi_include` takes about

20 seconds, while subsequent runs require less than 60 *milli*seconds.



### Showcase of advanced features

The presentation [From Mesh Generation to Adaptive Simulation: A Journey in Julia](https://youtu.be/_N4ozHr-t9E),

originally given as part of JuliaCon 2022, outlines how to use Trixi.jl for an adaptive simulation

of the compressible Euler equations in two spatial dimensions on a complex domain. More details

as well as code to run the simulation presented can be found at the

[reproducibility repository](https://github.com/trixi-framework/talk-2022-juliacon_toolchain)

for the presentation.



## Documentation

Additional documentation is available that contains more information on how to

modify/extend Trixi.jl's implementation, how to visualize output files etc. It

also includes a section on our preferred development workflow and some tips for

using Git. The latest documentation can be accessed either

[online](https://trixi-framework.github.io/Trixi.jl/stable) or under [`docs/src`](docs/src).



## Referencing

If you use Trixi.jl in your own research or write a paper using results obtained

with the help of Trixi.jl, please cite the following articles:

```bibtex

@article{ranocha2022adaptive,

  title={Adaptive numerical simulations with {T}rixi.jl:

         {A} case study of {J}ulia for scientific computing},

  author={Ranocha, Hendrik and Schlottke-Lakemper, Michael and Winters, Andrew Ross

          and Faulhaber, Erik and Chan, Jesse and Gassner, Gregor},

  journal={Proceedings of the JuliaCon Conferences},

  volume={1},

  number={1},

  pages={77},

  year={2022},

  doi={10.21105/jcon.00077},

  eprint={2108.06476},

  eprinttype={arXiv},

  eprintclass={cs.MS}

}



@article{schlottkelakemper2021purely,

  title={A purely hyperbolic discontinuous {G}alerkin approach for

         self-gravitating gas dynamics},

  author={Schlottke-Lakemper, Michael and Winters, Andrew R and

          Ranocha, Hendrik and Gassner, Gregor J},

  journal={Journal of Computational Physics},

  pages={110467},

  year={2021},

  month={06},

  volume={442},

  publisher={Elsevier},

  doi={10.1016/j.jcp.2021.110467},

  eprint={2008.10593},

  eprinttype={arXiv},

  eprintclass={math.NA}

}

```



In addition, you can also refer to Trixi.jl directly as

```bibtex

@misc{schlottkelakemper2020trixi,

  title={{T}rixi.jl: {A}daptive high-order numerical simulations

         of hyperbolic {PDE}s in {J}ulia},

  author={Schlottke-Lakemper, Michael and Gassner, Gregor J and

          Ranocha, Hendrik and Winters, Andrew R and Chan, Jesse},

  year={2021},

  month={09},

  howpublished={\url{https://github.com/trixi-framework/Trixi.jl}},

  doi={10.5281/zenodo.3996439}

}

```



## Authors

Trixi.jl was initiated by [Michael

Schlottke-Lakemper](https://www.uni-augsburg.de/fakultaet/mntf/math/prof/hpsc)

(University of Augsburg, Germany) and

[Gregor Gassner](https://www.mi.uni-koeln.de/NumSim/gregor-gassner)

(University of Cologne, Germany). Together with [Hendrik Ranocha](https://ranocha.de)

(Johannes Gutenberg University Mainz, Germany), [Andrew Winters](https://liu.se/en/employee/andwi94)

(Linköping University, Sweden), and [Jesse Chan](https://jlchan.github.io) (Rice University, US),

they are the principal developers of Trixi.jl.

The full list of contributors can be found in [AUTHORS.md](AUTHORS.md).



## License and contributing

Trixi.jl is licensed under the MIT license (see [LICENSE.md](LICENSE.md)). Since Trixi.jl is

an open-source project, we are very happy to accept contributions from the

community. Please refer to [CONTRIBUTING.md](CONTRIBUTING.md) for more details.

Note that we strive to be a friendly, inclusive open-source community and ask all members

of our community to adhere to our [`CODE_OF_CONDUCT.md`](CODE_OF_CONDUCT.md).

To get in touch with the developers,

[join us on Slack](https://join.slack.com/t/trixi-framework/shared_invite/zt-sgkc6ppw-6OXJqZAD5SPjBYqLd8MU~g)

or [create an issue](https://github.com/trixi-framework/Trixi.jl/issues/new).



## Acknowledgments






This project has benefited from funding by the [Deutsche

Forschungsgemeinschaft](https://www.dfg.de/) (DFG, German Research Foundation)

through the following grants:

* Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.

* Research unit FOR 5409 "Structure-Preserving Numerical Methods for Bulk- and

  Interface Coupling of Heterogeneous Models (SNuBIC)" (project number 463312734).

* Individual grant no. 528753982.



This project has benefited from funding from the [European Research Council](https://erc.europa.eu)

through the

ERC Starting Grant "An Exascale aware and Un-crashable Space-Time-Adaptive

Discontinuous Spectral Element Solver for Non-Linear Conservation Laws" (Extreme),

ERC grant agreement no. 714487.



This project has benefited from funding from [Vetenskapsrådet](https://www.vr.se)

(VR, Swedish Research Council), Sweden

through the VR Starting Grant "Shallow water flows including sediment transport and morphodynamics",

VR grant agreement 2020-03642 VR.



This project has benefited from funding from the United States

[National Science Foundation](https://www.nsf.gov/) (NSF) under awards

DMS-1719818 and DMS-1943186.



This project has benefited from funding from the German

[Federal Ministry of Education and Research](https://www.bmbf.de) (BMBF)

through the project grant "Adaptive earth system modeling

with significantly reduced computation time for exascale supercomputers

(ADAPTEX)" (funding id: 16ME0668K).



This project has benefited from funding by the

[Daimler und Benz Stiftung](https://www.daimler-benz-stiftung.de) (Daimler and Benz Foundation)

through grant no. 32-10/22.



Trixi.jl is supported by [NumFOCUS](https://numfocus.org/) as an Affiliated Project.