Publishing our methods is an important part of science—the codes here are a mix of teaching codes and research codes that I use for my work. Check out my github page too: https://github.com/zingale.

AMReX: I am a contributor and member of the Technical Committee for the AMReX adaptive mesh refinement library.
yt: I am a contributor to the yt analysis and visualization library.
VAST: I am an organizer of the Virtual Astronomy Software Talks seminar series.

Support for developing the codes here is provided by the Department of Energy Office of Nuclear Physics. Past support has included the Department of Energy Exascale Compute Project and the Department of Energy SciDAC Program.

Astrophysics Simulation Codes

Castro: compressible hydrodynamics
Castro is our fully compressible hydrodynamics code built on the adaptive mesh refinement library AMReX. It supports self-gravity, diffusion, general equations of state, nuclear reactions, and more.
MAESTROeX: low Mach number stratified flows
MAESTROeX is a low Mach number hydrodynamics code built on the AMReX library. It supports a general equation of state and is designed for problems involving stellar convection.
AMReX-Astro Microphysics
AMReX-Astro Microphysics is a collection of reaction networks, EOSes, and other physics modules for use in our AMReX-Astrophysics suite of hydrodynamics codes.

pyro: a python hydro code
pyro is a tutorial code designed to introduce new students into computational hydrodynamics. The python code implements 2-d solvers for linear advection, compressible hydrodynamics, multigrid, implicit diffusion, and incompressible hydrodynamics.
pynucastro: python for nuclear astrophysics
pynucastro interfaces to nuclear reaction rate databases and allows for the exploration of reaction networks and the output of network ODE righthand sides for integrating in a stellar physics code.
PPMpy: python piecewise parabolic method
ppmpy is a simple 1-d compressible hydrodynamics code that implements the piecewise parabolic method. It is written in python and has many methods to visualize the steps that PPM is taking in the reconstruction of the data.

Astronomy / Numerical Methods Education Codes

Intro astronomy animations
A set of introductory astronomy animations (Kepler's laws, Doppler shifts, parallax, ...) coded in python. These are also available on YouTube.

Computational Astro Jupyter Book
An interactive introduction to the core numerical methods used in astrophysics, including those for astrophysical simulations, written as a collection of Jupyter notebooks that can run in the cloud.

Godunov methods for linear advection
A simple 1-d second-order accurate finite-volume method for the linear advection equation. A choice of reconstruction is provided: Godunov (piecewise constant), piecewise linear, and piecewise parabolic (PPM). The code is structured to with the subroutines you would find in a typical hydrodynamics code.

Fortran version:
advect.f90
python version (no ppm):
advection.py
Multigrid examples
A simple python class for solving 1-d Poisson and constant-coefficient Helmholtz equations on a finite-volume grid. The driver program (mg_test.py) solves u_xx = sin(x), u(0)=0, u(1)=0. The discretization is second order (mg-converge.png).
multigrid solver github page
Also see pyro for a 2-d solver.
Diffusion
Simple 1-d second-order explicit and implicit diffusion codes. The implicit code uses a Crank-Nicolson time discretization and the banded matrix solver from SciPy.
diffusion_explicit.py
diffusion_implicit.py
Also see pyro for a 2-d solver.

2^nd order finite volume method for Burgers' equation
A simple second-order accurate finite-volume method for the 1-d Inviscid Burgers' Equation:
u_t + [1/2 u²]_x = 0
A choice of limiters is provided, and periodic BCs are implemented. The code is structured to with the subroutines you would find in a typical hydrodynamics code.
Fortran version:
burger.f90
python version:
burgers.py
Viscous Burgers' equation solver
Solve:
u_t + [ 1/2 u² ]_x = ε u_xx
using a second-order Godunov method for advection and Crank-Nicolson implicit diffusion for the viscous term. The two processes are coupled together.
burgervisc.py
Diffusion-reaction equation
Solve:
φ_t = κ φ_xx + (1/τ) R(φ)
using Crank-Nicolson diffusion and Strang-split reactions. This setup gives rises to a spreading burning front.
diffreact.py

OpenMP Relaxation Solver of Poisson's Equation
Solve the 2-d Poisson equation with pure relaxation (we do a fixed number of iterations). This is parallelized with OpenMP.
relax-omp.f90
MPI Relaxation Solver of Poisson's Equation
Solve the 2-d Poisson equation with pure relaxation (we do a fixed number of iterations). This is parallelized with MPI, doing a one-dimensional domain decomposition in the x direction.
relax-mpi.f90

Parallel I/O Tutorial
A simple parallel I/O tutorial showing various ways to output data from a parallel hydrodynamics code into a single HDF5 file.

Simple Backup Script
A simple script for automatically backing up several directories in your home directory to another disk mounted on your local system. To have this run automatically, set it up as a cron job.
backup-machine.py

Research Journal
A python script to manage a research journal / logbook in restructured text / Sphinx. It is distributed (uses git under the hood), so you can use it on all of the machines you work on and keep things in sync, and it is commandline driven, so the barrier to entry to make a journal entry is very low. It supports images in an entry, editing previous entries, and has simple sub-commands to build and display your web-based journal.
pyjournal2