Main Page

Slow streaks (blue) and vortex structures (yellow)

Overview

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

The flow of fluid through a straight pipe of circular cross-section is a simple and familiar set up, yet the flow exhibits rich chaotic dynamics. It provides a setting both for investigation of the principles of simulation, and 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, and subroutines for well-known methods are designed to be problem-independent. The core code is designed to be flexible yet very fast.

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.
• [From 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

Get the code here!

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 (please check here for latest citation info.):

            e.g. "using openpipeflow.org \cite{openpipeflow}."
               @TechReport{ openpipeflow,
                  author = "A.\ P.\ Willis",
                  title = "The openpipeflow.org {N}avier--{S}tokes solver",
                  publisher = "openpipeflow.org",
                  year = "2015",
                  note = "{openpipeflow.org/index.php?title=File:TheOpenpipeflowSolver.pdf}",
               }

            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.