<h1 align="center"> Dedalus Project </h1>  <p align="center"> <a href="https://www.repostatus.org/#active"> <img alt="Repo status" src="https://www.repostatus.org/badges/latest/active.svg" /> </a> <a href="http://dedalus-project.readthedocs.org"> <img alt="Read the Docs" src="https://img.shields.io/readthedocs/dedalus-project"> </a> <img alt="PyPI - Python Version" src="https://img.shields.io/pypi/pyversions/dedalus"> <a href="https://pypi.org/project/dedalus/"> <img alt="PyPI" src="https://img.shields.io/pypi/v/dedalus"> </a> <a href="https://github.com/conda-forge/dedalus-feedstock"> <img alt="Conda Version" src="https://img.shields.io/conda/vn/conda-forge/dedalus"> </a> <a href="https://www.gnu.org/licenses/gpl-3.0.en.html"> <img alt="PyPI - License" src="https://img.shields.io/pypi/l/dedalus"> </a> </p>

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 and boundary conditions enforced with the tau method, as:

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 for tutorials and additional examples.

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