This paper is devoted to the development and application of hybrid methods combining, on the one hand, semi-lagrangian methods for the advection-diffusion of scalars, and, on the other hand, either finite volume or spectral methods, depending on the flow geometry, for the Navier-Stokes equations. A particular focus is made on the accuracy and scalability of the methods. These methods are then used to study differential diffusion of scalars on two canonical cases: Homogeneous Isotropic Turbulence and a jet flow. We first characterize differential diffusion in terms of spectral distribution. We then use the Reynolds decomposition to bring out the different mechanisms involved in the energy budget of the scalar and we analyze their spatial distribution.

本文致力于混合方法的开发和应用，一方面是用于标量对流扩散的半拉格朗日方法，另一方面是根据流动几何形状的有限体积或谱方法。 , 对于 Navier-Stokes 方程。特别关注方法的准确性和可扩展性。然后，这些方法用于研究两种典型情况下标量的微分扩散：均质各向同性湍流和射流。我们首先根据光谱分布来表征微分扩散。然后我们使用雷诺分解来找出标量能量收支中涉及的不同机制，并分析它们的空间分布。