  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.
