Overlapping Domain Decomposition Applied to the Navier–Stokes Equations

  • Oana Ciobanu
  • Laurence Halpern
  • Xavier Juvigny
  • Juliette Ryan
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


A space-time domain decomposition algorithm for the compressible Navier–Stokes problem has been designed, with the aim of implementing it in three dimensions, in an industrial code. The system is discretised with a second order implicit scheme in time and Finite Volumes Method in space. To achieve full speedup performance, a Schwarz Waveform Relaxation method coupled with a Newton procedure is used, as it allows local space and time stepping. The performances of different parallelisation strategies (using OpenMP, MPI and GPUs) are compared in difficult configurations.


Adaptive time-stepping Compressible Navier–Stokes solver Direct numerical simulation Finite volumes method Newton-Schwarz method Schwarz waveform relaxation method Time-space domain decomposition 


  1. 1.
    X.-C. Cai, D.E. Keyes, Nonlinearly preconditioned inexact Newton algorithms. SIAM 24(1),183–200 (2002)MathSciNetMATHGoogle Scholar
  2. 2.
    T. Colonius, S.K. Lele, P. Moin, Sound generation in a mixing layer. J. Fluid Mech. 330,375–409 (1997)CrossRefMATHGoogle Scholar
  3. 3.
  4. 4.
    M.J. Gander, Overlapping Schwarz waveform relaxation for parabolic problems, in DD10 Proceedings, vol. 218 (1998), pp. 425–431Google Scholar
  5. 5.
    M.J. Gander, A.M. Stuart, Space-time continuous analysis of waveform relaxation for the heat equations. SIAM 19(6), 2014–2031 (1998)MathSciNetMATHGoogle Scholar
  6. 6.
    F. Haeberlein, Time-space domain decomposition methods for reactive transport. Ph.D. thesis, University Paris 13, 2011Google Scholar
  7. 7.
    F. Haeberlein, L. Halpern, Optimized Schwarz waveform relaxation for nonlinear systems of parabolic type, in DD21 Proceedings (2012)Google Scholar
  8. 8.
    L. Halpern, J. Ryan, M. Borrel, Domain decomposition vs. overset Chimera grid approaches for coupling CFD and CAA, in ICCFD7 (2012)Google Scholar
  9. 9.
    R. Jeltsch, B. Pohl, Waveform relaxation with overlapping splittings. SIAM 16(1), 40–49 (1995)MathSciNetMATHGoogle Scholar
  10. 10.
    D.E. Keyes, Domain decomposition in the mainstream of computational science, in DD14 Proceedings (2002)Google Scholar
  11. 11.
    D.A. Knoll, D.E. Keyes, Jacobian-free Newton–Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193(2), 357–397 (2004)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    E. Lelarasmee, A.E. Ruehli, A.L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE 1(3), 131–145 (1982)Google Scholar
  13. 13.
    M.-S. Liou, A sequel to AUSM, part II: AUSM+-up for all speeds. J. Comput. Phys. 214(1), 137–170 (2006)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    B. Ong, S. High, F. Kwok, Pipeline Schwarz waveform relaxation, in 22nd DDM Conference (2013, submitted)Google Scholar
  15. 15.
    H.C. Yee, N.D. Sandham, M.J. Djomehri, Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150(1), 199–238 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Oana Ciobanu
    • 1
  • Laurence Halpern
    • 2
  • Xavier Juvigny
    • 1
  • Juliette Ryan
    • 1
  1. 1.ONERAChatillonFrance
  2. 2.Université Paris 13, LAGAVilletaneuseFrance

Personalised recommendations