Main Page

Slow streaks (blue) and vortex structures (yellow)

Overview

openpipeflow.org is a free resource for researchers, engineers, educators and the interested public.

• Flow through a pipe is a conveniently simple set up, demonstrating rich chaotic dynamics.
• The codes provided on this site may be used to investigate the principles of simulation, or to provide a setting for methods designed to probe the fundamental properties of dynamical systems.
• The majority of mathematical techniques described on these pages are applicable to a huge range of problems. The core code is designed to be flexible, yet very fast, and subroutines for well-known methods are designed to be problem-independent.

Aims

• To make accessible a range of modelling techniques.
• To facilitate rapid entry into the world of numerical simulation and fluid dynamics.
• To provide flexible modules for more the use and development of advanced techniques in research.

Code features

• Primitive-variable pipe-flow code for incompressible flow.
• Simple scripts for visualisation with Matlab/Octave/Visit.
• May be run on a single core or in parallel (with MPI). Essentially linear scaling with number of cores.
• [NEW July 2015] '2-dimensional' parallelisation, radial+axial split.
• Readable Fortran 90, uses modules and derived types, no esoteric extensions.
• Core program <3000 lines.
• Spatial discretisation: double-Fourier (theta,z) + finite difference (r).
• PPE formulation; influence matrix corrects boundary conditions to machine precision.
• Second-order predictor-corrector method, automatic timestep control.

Manual, Tutorial, FAQ

Links to the Manual, Tutorial and FAQ can be found on the left sidebar.

The Manual covers

• setup and typical usage of the code,
• definition of the model,
• mathematics behind the methods,
• conventions used in the code,
• description of utility codes.

The Tutorial guides a new user through

• setting up parameters for a job,
• monitoring a job's progress,
• simple plotting of time series from a run,
• visualisation of structures in a snapshot,
• manipulating data.

Download

Follow link here or on left side-bar.

Database

The Database provides sample parameters and initial conditions from which to launch new simulations. In general, simulations start most reliably from an initial state computed for similar parameters. A range of starting points are provided.

Features to appear/wishlist

• Utilities for Krylov methods -- Newton-Krylov, Arnoldi.
• Module for the immersed boundary method (IBM).
• More FAQ + documentation.

Citation

• In talks:

               openpipeflow.org

• In articles:

               e.g. "using openpipeflow.org, based on code described in \cite{WK09}."
                  @article{WK09,
                       Author = {A. P. Willis and R. R. Kerswell},
                       Year = {2009},
                       Title = {Turbulent dynamics of pipe flow captured in a
                               reduced model: puff relaminarisation and
                               localised `edge' states},
                       Journal = {J.\ Fluid Mech.},
                       Volume = {619},
                       Pages = {213-233}  }

Author

Ashley P. Willis,

School of Mathematics and Statistics (SoMaS),

University of Sheffield, U.K.

ashleypwillis/at/gmail.com

Thanks

• John Gibson (channelflow.org)
• Predrag Cvitanović (GaTech chaosbook.org)
• Rich Kerswell (Bristol)
• many other people!
• EPSRC GR/S76144/01, EP/K03636X/1
• The University of Sheffield.