In this work, we propose a model for the orientation of inertialess spheroidal particles suspended in turbulent flows. This model consists in a stochastic version of the Jeffery equation that can be included in a statistical Lagrangian description of particles suspended in a flow. It is compatible and coherent with turbulence models that are widely used in CFD codes for the simulation of the flow field in practical large-scale applications. In this context, we propose and analyze a numerical scheme based on a splitting scheme algorithm that decouples the orientation dynamics into its main contributions: stretching and rotation. We detail its implementation in an open-source CFD software. We analyze the weak and strong convergence of both the global scheme and of each sub-part. Subsequently, the splitting technique yields to a highly efficient hybrid algorithm coupling pure probabilistic and deterministic numerical schemes. Various numerical experiments were implemented and the results were compared with analytical predictions of the model to assess the algorithm efficiency and accuracy.

翻译：本文提出一种悬浮于湍流中无惯性椭球粒子取向的模型。该模型由杰弗里方程的随机版本构成，可纳入悬浮粒子的统计拉格朗日描述框架。模型与广泛用于大规模工程应用流场模拟的CFD湍流模型兼容且一致。在此背景下，我们提出并分析了一种基于分裂算法的数值方案，将取向动力学解耦为拉伸与旋转两项主要贡献。详细阐述了该算法在开源CFD软件中的实现过程，并分别对全局方案及其子模块的弱收敛性与强收敛性进行了分析。分裂技术进一步衍生出融合纯概率与确定性数值方法的高效混合算法。通过开展多组数值实验，将计算结果与模型解析预测进行对比，验证了算法的效率与精度。