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/

• 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.

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.

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

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

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

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