Keywords: fresh concrete flow, non-Newtonian fluids, homogenization.

The understanding and modelling of flow in porous media is important in many engineering problems, including waste disposal and groundwater management, fresh concrete casting, or porous rock flows. When modelling fluid flow in heterogeneous media, it is generally not possible to account for all phenomena occurring at various length scales. Instead, a sequence of models operating at corresponding resolution levels is created, supplemented by appropriate up and down scaling techniques to interconnect individualmodels. In practical simulations, it is usually sufficient to predict macroscopic properties or behavior. The chapter will present a state-of-the–art review of availablemultiscalemethods in the area of heterogeneous media flows with application to fresh concrete flow and particularly how the effect of traditional reinforcement can be taken into account. First, it will be shown how the Darcy law can be derived from the homogenization of a stationary Navier-Stokes system. Later, we provide an overview of generalization of this result to non-Newtonian fluids, as the fresh concrete can on the macroscale be considered as a non-Newtonian fluid. In the last part, the results of modelling the effect of reinforcing bars in the single-fluid approach by means of computational homogenization will be presented.

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