Multi-scale Problems, High Performance Computing and Hybrid Numerical Methods

  • G. Balarac
  • G. -H. Cottet
  • J. -M. Etancelin
  • J. -B. Lagaert
  • F. Perignon
  • C. Picard
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)


The turbulent transport of a passive scalar is an important and challenging problem in many applications in fluid mechanics. It involves different range of scales in the fluid and in the scalar and requires important computational resources. In this work we show how hybrid numerical methods, combining Eulerian and Lagrangian schemes, are natural tools to address this mutli-scale problem. One in particular shows that in homogeneous turbulence experiments at various Schmidt numbers these methods allow to recover the theoretical predictions of universal scaling at a minimal cost. We also outline how hybrid methods can take advantage of heterogeneous platforms combining CPU and GPU processors.


High performance computing Particle method Hybrid computing Turbulence Transport equations 



This work was partially supported by the Agence Nationale pour la Recherche (ANR) under Contracts No. ANR-2010-JCJC-091601 and ANR-2010-COSI-0009. G.-H. C. is also grateful for the support from Institut Universitaire de France. Computations reported in Sect. 3 were performed using HPC resources from GENCI-IDRIS (Grant 2012-020611).


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  • G. Balarac
    • 1
  • G. -H. Cottet
    • 2
  • J. -M. Etancelin
    • 2
  • J. -B. Lagaert
    • 3
  • F. Perignon
    • 2
  • C. Picard
    • 2
  1. 1.LEGICNRS and Université de GrenobleGrenoble Cedex 9France
  2. 2.Laboratoire Jean KuntzmannCNRS and Université de GrenobleGrenoble Cedex 9France
  3. 3.Laboratoire de MathématiquesUniversité Paris 11Orsay CedexFrance

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