This work is funded under the embedded CSE programme of the ARCHER UK National Supercomputing Service.

HemeLB [1] is code designed to simulate blood flow in arteries using Lattice-Boltzmann methods (LBM). For complex geometries like the Circle of Willis, it scales up to 25k cores on the Cray XC30 supercomputer ARCHER but simulations still take several days to complete. Building on the work by Randles and Kaxiras [2], this project will integrate parallel-in-time integration capacities into HemeLB to extend scaling and reduce wall-clock times.

The aims of the project are:

  1. Implement the Parareal [3] algorithm into HemeLB to provide parallel-in-time integration capacities.
  2. Optimise communication and scheduling in time to minimise overheads and improve efficiency and resource utilisation of Parareal.
  3. Demonstrate speedup of five or better using the Circle of Willis simulation model, thus bringing simulations times down to a day or less.
  4. Simplify and automate the Parallel-In-Time implementation, allowing others in the community to perform these runs with a single-line command using FabSim.
  5. Continuously provide information about the employed parallel-in-time approach to the ARCHER community to facilitate adoption for other codes.
  1. D. Groen, J. Hetherington, H. B. Carver, R. W. Nash, M. O. Bernabeu, and P. V. Coveney, “Analysing and modelling the performance of the HemeLB lattice-Boltzmann simulation environment,” Journal of Computational Science, vol. 4, no. 5, pp. 412–422, 2013 [Online]. Available at:
      author = {Groen, Derek and Hetherington, James and Carver, Hywel B and Nash, Rupert W and Bernabeu, Miguel O and Coveney, Peter V},
      url = {},
      journal = {Journal of Computational Science},
      number = {5},
      pages = {412--422},
      title = {Analysing and modelling the performance of the HemeLB lattice-Boltzmann simulation environment},
      volume = {4},
      year = {2013}
  1. J.-L. Lions, Y. Maday, and G. Turinici, “A ‘parareal’ in time discretization of PDE’s,” Comptes Rendus de l’Académie des Sciences - Series I - Mathematics, vol. 332, pp. 661–668, 2001 [Online]. Available at:
      author = {Lions, J.-L. and Maday, Yvon and Turinici, Gabriel},
      journal = {Comptes Rendus de l'Académie des Sciences - Series I - Mathematics},
      pages = {661--668},
      title = {{A "parareal" in time discretization of {PDE}'s}},
      url = {},
      volume = {332},
      year = {2001}
  2. A. Randles and E. Kaxiras, “Parallel in time approximation of the lattice Boltzmann method for laminar flows,” Journal of Computational Physics, vol. 270, pp. 577–586, 2014 [Online]. Available at:
      author = {Randles, Amanda and Kaxiras, Efthimios},
      journal = {Journal of Computational Physics},
      pages = {577--586},
      title = {{Parallel in time approximation of the lattice {B}oltzmann method for laminar flows}},
      url = {},
      volume = {270},
      year = {2014}