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

Abstract The turbulent transport of a passive scalar is an important and challeng-ing problem in many applications in fluid mechanics. It involves different range of scales in the fluid and in the scalar and requires important computational re-sources. 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 scal-ing at a minimal cost. We also outline how hybrid methods can take advantage of heterogeneous platforms combining CPU and GPU processors.