Multi-scale problems, high performance computing and hybrid numerical methods

Guillaume Balarac, Georges-Henri Cottet, Jean-Mathieu Etancelin, Jean-Baptiste Lagaert, Franck Perignon, Christophe Picard
LEGI, CNRS and Universite de Grenoble
hal-00949669, (21 February 2014)




   title={Multi-scale problems, high performance computing and hybrid numerical methods},


   affiliation={Laboratoire des {‘e}coulements g{‘e}ophysiques et industriels – LEGI , Laboratoire Jean Kuntzmann – LJK , Laboratoire de Math{‘e}matiques d’Orsay – LMO},

   booktitle={The Impact of Applications on Mathematics -Proceedings of Forum "Math-for-Industry" 2013},


   pages={11 p.},

   address={Fukuoka, Japon},






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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 multi-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 hybrid methods can take advantage of heterogeneous platforms combining CPU and GPU processors.
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