Computational fluid dynamics (CFD) simulations containing freely moving bodies are still a challenging topic. More so, if the bodies are large enough to affect the fluid flow and distributed densely enough to come in contact both with the boundaries of the computational domain and with each other. In this work, we concentrate on the topic of simulation of (i) irregular bodies with flow-induced movement and contact with computational domain boundaries taken into account, and (ii) bodies entrained by the fluid and coming in contact not only with the domain boundaries but also with each other. The developed modeling approach is based on the hybrid fictitious domain-immersed boundary method extended by the discrete element method. The present contribution is focused on presentation of simulation principles and results of initial benchmark cases.

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Proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) have become established tools for model order reduction in simulations of fluid flows. However, including moving solid bodies in the computational domain poses additional issues with respect to the fluid-solid coupling and to the solution of the movement of the solids. Still, it seems that if the hybrid fictitious domain-immersed boundary method is used to include the solids in the flow domain, POD-DEIM based approaches may be extended for four-way coupled particleladen flows. The present work focuses on the construction of POD-DEIM based reduced order models for the aforementioned flows.

The present work is focused on improving the efficiency of a computational fluid dynamics (CFD) – discrete element method (DEM) solver allowing for computations with non-spherical solids. In general, the combination of CFD and DEM allows for simulations of freely moving solid particles within a computational domain containing fluid. The standard approach of CFD-DEM solvers is to approximate solid bodies by spheres, the geometry of which can be fully defined via its radius and center position. Consequently, the standard DEM contact models are based on an overlap depth between particles, which can be easily evaluated for a sphere-sphere contact. However, for a contact between two non-spherical particles, the overlap depth cannot be used and has to be replaced by the more general overlap volume. The precision of the overlap volume computation is (i) crucial for the correct evaluation of contact forces, and (ii) directly dependent on the computational mesh resolution. Still, the contact volume evaluation in DEM for arbitrarily shaped bodies is usually by at least one order of magnitude more demanding on the mesh resolution than the CFD. In order to improve the computational efficiency of our CFD-DEM solver, we introduce the concept of an OCTREEbased virtual mesh, in which the DEM spatial discretization is adaptively refined while the CFD mesh remains unchanged.