Lagrangian stochastic model for the orientation of inertialess non spherical particles in turbulent flows: an efficient numerical method for CFD approach

In this work, we propose a model for the orientation of non-spherical particles arising in multi-phase turbulence flow. This model addresses the macroscopic scale in use in CFD codes enabling turbulence models for the fluid phase. It consists in a stochastic version of the Jeffery equation that can be incorporated in a statistical Lagrangian description of the particles suspended in the flow. For use in this context, we propose and analyse a numerical scheme based on the well-known splitting scheme algorithm decoupling the orientation dynamics into their main contributions: stretching and rotation. We detail the implementation in an open-source CFD software. We analyse the weak and strong convergence both of the global scheme and of their sub-parts. Subsequently, the splitting technique yields to a highly efficient hybrid algorithm coupling pure probabilistic and deterministic numerical schemes. Various experiments were implemented and compared with analytic predictions of the model to test the scheme for use in a CFD code.