pyranda

A Python driven, Fortran powered Finite Difference solver for arbitrary hyperbolic PDE systems. This is the mini-app for the Miranda code.

The PDE solver defaults to a 10th order compact finite difference method for spatial derivatives, and a 5-stage, 4th order Runge-Kutta scheme for temporal integration. Other numerical methods will be added in the future.

Pyranda parses (through a simple interpreter) the full definition of a system of PDEs, namely:

• a domain and discretization (in 1D, 2D or 3D)
• governing equations written on RHS of time derivatives.
• initial values for all variables
• boundary conditions

Prerequisites

At a minimum, your system will need the following installed to run pyranda. See INSTALL.md for the detailed flows.

• A fortran compiler with MPI support
• Python 3
• numpy
• scipy
• matplotlib
• mpi4py

Install

On toss_4_x86_64, use the host-specific bootstrap scripts in scripts/. On this machine, the following command completed successfully:

BOOTSTRAP_VENV_ARGS=--system-site-packages bash scripts/bootstrap_toss_4_x86_64_ib.sh myEnv
source myEnv/bin/activate

The plain bootstrap without --system-site-packages built mpi4py successfully but then failed when the configured package index was unreachable for matplotlib. The bootstrap rebuilds mpi4py from source by default; set PYRANDA_MPI4PY_MODE=reuse if you explicitly want to reuse an existing importable mpi4py.

For non-toss_4_x86_64 environments, install the dependencies from requirements.txt first and then install pyranda without build isolation:

python -m pip install -r requirements.txt
python -m pip install --no-build-isolation .

A quick headless smoke test after installation is:

MPLBACKEND=Agg MPLCONFIGDIR=${MPLCONFIGDIR:-/tmp/mpl-pyranda} python examples/advection.py 32 1

Tutorials

A few tutorials are included on the project wiki page that cover the example below, as well as few others. A great place to start if you want to discover what types of problems you can solve.

Example Usage - Solve the 1D advection equation in less than 10 lines of code

The one-dimensional advection equation is written as:

where phi is a scalar and where c is the advection velocity, assumed to be unity. We solve this equation in 1D, in the x-direction from (0,1) using 100 points and evolve the solution .1 units in time.

1 - Import pyranda

from pyranda import pyrandaSim

2 - Initialize a simulation object on a domain/mesh

pysim = pyrandaSim('advection',"xdom = (0.0 , 1.0 , 100 )")

3 - Define the equations of motion

pysim.EOM(" ddt(:phi:) = - ddx(:phi:) ")

4 - Initialize variables

pysim.setIC(":phi: = 1.0 + 0.1 * exp( -(abs(meshx-.5)/.1 )**2 )")

5 - Integrate in time

dt = .001
time = 0.0
while time < .1:
   time = pysim.rk4(time,dt)

6 - Plot the solution

pysim.plot.plot('phi')

Cite

Please us the folowing bibtex, when you refer to this project.

  @misc{pyrandaCode,
    title  = {Pyranda: A Python driven, Fortran powered Finite Difference solver for arbitrary hyperbolic PDE systems and mini-app for the LLNL Miranda code},
    author = {Olson, Britton},
    url    = https://github.com/LLNL/pyranda},
    year   = {2023}
  }