pyro

A simple python-based tutorial on computational methods for hydrodynamics

pyro is a computational hydrodynamics code that presents two-dimensional solvers for advection, compressible hydrodynamics, diffusion, incompressible hydrodynamics, and multigrid, all in a finite-volume framework. The code is mainly written in python and is designed with simplicity in mind. The algorithms are written to encourage experimentation and allow for self-learning of these code methods.

The latest version of pyro is always available at:

https://github.com/zingale/pyro2

The project webpage, where you'll find documentation, plots, notes, etc. is here:

http://bender.astro.sunysb.edu/hydro_by_example/

Getting Started

• There are a few steps to take to get things running. You need to make sure you have numpy, f2py, and matplotlib installed. On a Fedora system, this can be accomplished by doing:

  yum install numpy numpy-f2py python-matplotlib python-matplotlib-tk

• You also need to make sure gfortran is present on you system. On a Fedora system, it can be installed as:

  yum install gcc-gfortran

• Not all matplotlib backends allow for the interactive plotting as pyro is run. One that does is the TkAgg backend. This can be made the default by creating a file ~/.matplotlib/matplotlibrc with the content:

  backend: TkAgg

  You can check what backend is your current default in python via:

  import matplotlib.pyplot 
  print matplotlib.pyplot.get_backend() 

• The remaining steps are:

  • Set the PYTHONPATH environment variable to point to the pyro2/ directory.

  • Build the Fortran source. In pyro2/ type

    ./mk.sh

  • Run a quick test of the advection solver:

    ./pyro.py advection smooth inputs.smooth

    you should see a graphing window pop up with a smooth pulse advecting diagonally through the periodic domain.

Solvers

pyro provides the following solvers (all in 2-d):

• advection: a second-order unsplit linear advection solver. This is the basic method to understand hydrodynamics.

• compressible: a second-order unsplit solver for the Euler equations of compressible hydrodynamics. This uses a 2-shock approximate Riemann solver.

• incompressible: a second-order cell-centered approximate projection method for the incompressible equations of hydrodynamics.

• diffusion: a Crank-Nicolson time-discretized solver for the constant-coefficient diffusion equation.

• multigrid: a cell-centered multigrid solver for a constant-coefficient Helmholtz equation, as well as a variable-coefficient Poisson equation (which inherits from the constant-coefficient solver).

• LM_atmosphere: (in development) a solver for the equations of low Mach number hydrodynamics for atmospheric flows.

• LM_combustion: (in development) a solver for the equations of low Mach number hydrodynamics for smallscale combustion.

Working With Data

In addition to the main pyro program, there are many analysis tools that we describe here. Note: some problems write a report at the end of the simulation specifying the analysis routines that can be used with their data.

• compare.py: this takes two simulation output files as input and compares zone-by-zone for exact agreement. This is used as part of the regression testing.

  usage: ./compare.py file1 file2

• plot.py: this takes the solver name and an output file as input and plots the data using the solver's dovis method.

  usage: ./plot.py solvername file

• analysis/

  • gauss_diffusion_compare.py: this is for the diffusion solver's Gaussian diffusion problem. It takes a sequence of output files as arguments, computes the angle-average, and the plots the resulting points over the analytic solution for comparison with the exact result.

    usage: ./gauss_diffusion_compare.py file*

  • incomp_converge_error.py: this is for the incompressible solver's converge problem. This takes a single output file as input and compares the velocity field to the analytic solution, reporting the L2 norm of the error.

    usage: ./incomp_converge_error.py file

  • plotvar.py: this takes a single output file and a variable name and plots the data for that variable.

    usage: ./plotvar.py file variable

  • sedov_compare.py: this takes an output file from the compressible Sedov problem, computes the angle-average profile of the solution and plots it together with the analytic data (read in from cylindrical-sedov.out).

    usage: ./sedov_compare.py file

  • smooth_error.py: this takes an output file from the advection solver's smooth problem and compares to the analytic solution, outputting the L2 norm of the error.

    usage: ./smooth_error.py file

  • sod_compare.py: this takes an output file from the compressible Sod problem and plots a slice through the domain over the analytic solution (read in from sod-exact.out).

    usage: ./sod_compare.py file

Understanding the algorithms

There is a set of notes that describe the background and details of the algorithms that pyro implements:

http://bender.astro.sunysb.edu/hydro_by_example/CompHydroTutorial.pdf

The source for these notes is also available on github:

https://github.com/zingale/numerical_exercises

Getting Help

Join the mailing list to say up-to-date:

http://bender.astro.sunysb.edu/mailman/listinfo/pyro-help