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dedalus

★ 703 Open GitHub ↗

A flexible framework for solving PDEs with modern spectral methods.

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<h1 align="center">
  Dedalus Project
</h1>

<p align="center">
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  <img alt="Conda Version" src="https://img.shields.io/conda/vn/conda-forge/dedalus">
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Dedalus is a flexible framework for solving partial differential equations using modern spectral methods.
The code is open-source and developed by a team of researchers studying astrophysical, geophysical, and biological fluid dynamics.

Dedalus is written primarily in Python and features an easy-to-use interface with symbolic vectorial equation specification.
For example, to simulate incompressible hydrodynamics in a ball, you can symbolically enter the equations, including [gauge conditions](https://dedalus-project.readthedocs.io/en/latest/pages/gauge_conditions.html) and [boundary conditions enforced with the tau method](https://dedalus-project.readthedocs.io/en/latest/pages/tau_method.html), as:

```python
problem.add_equation("div(u) + tau_p = 0")
problem.add_equation("dt(u) - nu*lap(u) + grad(p) + lift(tau_u) = - u@grad(u)")
problem.add_equation("u(r=1) = 0")
problem.add_equation("integ(p) = 0")
```

Our numerical algorithms produce sparse and spectrally accurate discretizations of PDEs on simple domains, including Cartesian domains of any dimension, disks, annuli, spheres, spherical shells, and balls:

<table style="background-color:#FFFFFF;">
  <tr>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_1d_kdv_burgers.html">
        <figure>
          <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/kdv_burgers.png">
          <figcaption>KdV-Burgers equation (1D IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_2d_rayleigh_benard.html">
        <figure>
          <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/rayleigh_benard.png">
          <figcaption>Rayleigh-Benard convection (2D IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_2d_shear_flow.html">
        <figure>
            <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/shear_flow.png">
            <figcaption>Periodic shear flow (2D IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/lbvp_2d_poisson.html">
        <figure>
            <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/poisson.png">
            <figcaption>Poisson equation (2D LBVP)</figcaption>
        </figure>
      </a>
    </th>
  </tr>
  <tr>
  </tr>
  <tr>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_disk_libration.html">
        <figure>
          <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/libration.png">
          <figcaption>Librational instability (disk IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_sphere_shallow_water.html">
        <figure>
          <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/shallow_water.png">
          <figcaption>Spherical shallow water (sphere IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_shell_convection.html">
        <figure>
            <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/shell_convection.png">
            <figcaption>Spherical shell convection (shell IVP)</figcaption>
        </figure>
      </a>
    </th>
    <th width="25%">
      <a href="https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_ball_internally_heated_convection.html">
        <figure>
            <img src="https://raw.githubusercontent.com/DedalusProject/dedalus/master/docs/pages/examples/images/internally_heated_convection.png">
            <figcaption>Internally heated convection (ball IVP)</figcaption>
        </figure>
      </a>
    </th>
  </tr>
</table>

The resulting systems are efficiently solved using compiled libraries and are automatically parallelized using MPI.
See the [documentation](http://dedalus-project.readthedocs.org) for tutorials and additional examples.

## Links

* Project homepage: <http://dedalus-project.org>
* Code repository: <https://github.com/DedalusProject/dedalus>
* Documentation: <http://dedalus-project.readthedocs.org>
* Mailing list: <https://groups.google.com/forum/#!forum/dedalus-users>

## Developers

* [Keaton Burns (@kburns)](https://github.com/kburns)
* [Geoff Vasil (@geoffvasil)](https://github.com/geoffvasil)
* [Jeff Oishi (@jsoishi)](https://github.com/jsoishi)
* [Daniel Lecoanet (@lecoanet)](https://github.com/lecoanet/)
* [Ben Brown (@bpbrown)](https://github.com/bpbrown)

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