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Slow streaks (blue) and vortex structures (yellow)


Download | Manual | Tutorial | Database

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

Pipe flow is a simple and familiar set up, yet the flow patterns exhibit rich chaotic dynamics. This provides a setting for investigating the principles of simulation at one level, and at another, for developing new methods designed to probe 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 callable from any code. The core pipe flow code is designed to be flexible yet very fast.


  • 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.
  • 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.
  • May be run on a single core or in parallel (with MPI). Essentially linear scaling with number of cores.
  • '2-dimensional' parallelisation, radial+axial split.
  • Jacobian-Free Newton-Krylov (JFNK) solver. Now at .

Details for the above can be found in the Manual. This article, File:TheOpenpipeflowSolver.pdf, provides an overview of the code and its context.


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

  • Module for the immersed boundary method (IBM).
  • More FAQ + documentation.


Please cite this article: File:TheOpenpipeflowSolver.pdf


Ashley P. Willis,
School of Mathematics and Statistics (SoMaS),
University of Sheffield, U.K.