We investigate the reactive flow through a fixed bed of catalyst particles. Our simulation method belongs to the class of multi-scale approaches and combines nano scale DFT (Density Functional Theory) computations, mean-field kinetics at the micro scale and fully-resolved hydrodynamic simulations at the millimetric scale. At this stage, the simulations at the chemical (nano and micro) scales provide the rate constants needed by the hydrodynamic model in a one-way coupling. In this paper, we focus on the fully-resolved millimetric scale simulation model based on a Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) method combined with a Finite Volume/Staggered Grid scheme and a high order reconstruction at the fluid/solid interface. In particular, we present various DLM/FD algorithms that supply a divergence free velocity field, a property crucial for the accurate discretization of the additional diffusion-convection equations modeling the chemical reactions. Our method is implemented in our fully MPI platform PeliGRIFF (www.peligriff.com) dedicated to the multi-scale simulation of flows with particles/bubbles/drops. We illustrate the assets of our simulation method on the reactive flow through a pack of 3D cylinders and discuss the forthcoming developments required to extend our approach to a two-way coupling in which the reaction rates are affected by the flow dynamics.

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