The study's ultimate goal consists of modelling and optimising the co-digestion of particulate substrates like sewage sludge, biowaste and vinasse from sugar cane. Given these substrates, the medium is highly heterogeneous and has particular physical characteristics and behaviour. Moreover, anaerobic digestion could be lead in wet-mode or in dry-mode, thus we want to develop a model valid for both configurations. In this context, the fluid flow modelling is of interest. Indeed, the contact between substrates and microorganisms has a significant influence on the anaerobic digestion process. It is directly correlated to the flow inside the digester. The research question is therefore the following: Is it possible to predict the spread of microorganisms inside the digester for both liquid and solid digestion? In this paper, we present the context of the work and the mathematical model based on Navier-Stokes equations with the Boussinesq approximation. Large-eddy simulation (LES) is used for the turbulence modelling. The sliding mesh method is used to characterise the impeller rotation. In further work, we will present the simulation results validated with the literature data. The differential equations will be solved on OpenFOAM software using the finite volume method. The flow will be simulated for both Newtonian (vinasse) and non-Newtonian fluids (manure) and at different total solid (TS) rates for non-Newtonian fluids. The obtained results will be the velocity and temperature profiles within the digester. It will hence be possible to optimise the process through both the medium physical properties (TS rate and viscosity) and the digester configuration. We will also consider the multiphase flow. Alongside numerical simulations, experiments are carried out on the substrates studied in order to estimate the methane production. In this article, we present the results of experiments on the vinasse and the development of the CFD model.