Trixi.jl

Trixi.jl is a numerical simulation framework for hyperbolic conservation laws written in Julia. 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 is focused on being easy to use for new or inexperienced users, including the installation and postprocessing procedures. Its features include:

• Hierarchical quadtree/octree grid with adaptive mesh refinement
• Native support for 2D and 3D simulations
• High-order accuracy in space in time
• Nodal discontinuous Galerkin spectral element methods
  • Kinetic energy-preserving and entropy-stable split forms
  • Entropy-stable shock capturing
  • Positivity-preserving limiting
• Explicit low-storage Runge-Kutta time integration
• Square/cubic domains with periodic and weakly-enforced boundary conditions
• Multiple governing equations:
  • Compressible Euler equations
  • Magnetohydrodynamics equations
  • Hyperbolic diffusion equations for elliptic problems
  • Scalar advection
• Multi-physics simulations
  • Self-gravitating gas dynamics
• Shared-memory parallelization via multithreading
• Visualization of results with Julia-only tools (2D) or ParaView/VisIt (2D/3D)

Installation

If you have not yet installed Julia, please follow the instructions for your operating system. Trixi works with Julia v1.5.

For users

Trixi and related postprocessing tools are registered Julia packages. Hence, you can install Trixi, Trixi2Vtk, and Trixi2Img by executing the following commands in the Julia REPL:

julia> import Pkg

julia> Pkg.add("Trixi"); Pkg.add("Trixi2Vtk"); Pkg.add("Trixi2Img")

Note that you can copy and paste all commands to the REPL including the leading julia> prompts - they will automatically be stripped away by Julia.

For developers

If you plan on editing Trixi itself, you can download Trixi locally and run it from within the cloned directory:

git clone [email protected]:trixi-framework/Trixi.jl.git
cd Trixi.jl
julia --project=. -e 'import Pkg; Pkg.instantiate()' # Install Trixi's dependencies
julia -e 'import Pkg; Pkg.add("Trixi2Vtk"); Pkg.add("Trixi2Img")' # Install postprocessing tools

If you installed Trixi this way, you always have to start Julia with the --project flag set to your local Trixi clone, e.g.,

julia --project=.

Further details can be found in the documentation.

Usage

In the Julia REPL, first load the package Trixi

julia> using Trixi

Then start a simulation by executing

julia> Trixi.run(default_example())

To visualize the results, load the package Trixi2Img

julia> using Trixi2Img

and generate a contour plot of the results with

julia> trixi2img(joinpath("out", "solution_000040.h5"), output_directory="out", grid_lines=true)

This will create a file solution_000040_scalar.png in the out/ subdirectory that can be opened with any image viewer:

The method Trixi.run(...) expects a single string argument with the path to a Trixi parameter file. To quickly see Trixi in action, default_example() returns the path to an example parameter file with a short, two-dimensional problem setup. A list of all example parameter files packaged with Trixi can be obtained by running get_examples(). Alternatively, you can also browse the examples/ subdirectory. If you want to modify one of the parameter files to set up your own simulation, download it to your machine, edit the configuration, and pass the file path to Trixi.run(...).

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.run takes about 15 seconds, while subsequent runs require less than 50 milliseconds.

Documentation

Additional documentation is available that contains more information on how to modify/extend Trixi'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 or under docs/src.

Referencing

If you use Trixi in your own research or write a paper using results obtained with the help of Trixi, please cite the following paper:

@online{schlottkelakemper2020purely,
  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},
  year={2020},
  month={08},
  eprint={2008.10593},
  eprinttype={arXiv},
  eprintclass={math.NA}
}

In addition, you can also refer to Trixi directly as

@misc{schlottkelakemper2020trixi,
  title={{T}rixi.jl: A tree-based numerical simulation framework
         for hyperbolic {PDE}s written in {J}ulia},
  author={Schlottke-Lakemper, Michael and Gassner, Gregor J and
          Ranocha, Hendrik and Winters, Andrew R},
  year={2020},
  month={08},
  howpublished={\url{https://github.com/trixi-framework/Trixi.jl}},
  doi={10.5281/zenodo.3996439}
}

Authors

Trixi was initiated by Michael Schlottke-Lakemper and Gregor Gassner (both University of Cologne, Germany). Together with Hendrik Ranocha (KAUST, Saudi Arabia) and Andrew Winters (Linköping University, Sweden), they are the principal developers of Trixi. The full list of contributors can be found in AUTHORS.md.

License and contributing

Trixi is licensed under the MIT license (see LICENSE.md). Since Trixi is an open-source project, we are very happy to accept contributions from the community. Please refer to CONTRIBUTING.md for more details.