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

Abstract : 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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Guillaume Balarac, Georges-Henri Cottet, Jean-Matthieu Etancelin, Jean-Baptiste Lagaert, Franck Pérignon, et al.. Multi-scale problems, high performance computing and hybrid numerical methods. The Impact of Applications on Mathematics -Proceedings of Forum “Math-for-Industry”, Nov 2013, Fukuoka, Japan. pp.245-255, ⟨10.1007/978-4-431-54907-9_18⟩. ⟨hal-00949669v2⟩

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