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A coupled FEM–DEM method for the modeling of fluids laden with particles

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Abstract

This work presents a computational method for the solution of problems involving flowing fluid media laden with solid particles. The idea is based on previous works by the authors on (though then separately considered) fluid–structure interaction and particle dynamics. The fluid problem is treated through an Eulerian finite element approach, with the resulting system of nonlinear equations being iteratively solved by a Newton–Raphson procedure within a Newmark time integration scheme. The particle problem, in turn, is treated through a Lagrangian discrete element approach, wherein both particle-to-particle and particle-to-wall (rigid surfaces) contacts are fully permitted and resolved. The influence of the fluid on the motion of the particles is represented by means of forces and moments, which are computed from solution of the fluid flow around the particles and imposed on the latter in a coupled iterative way. The influence of the particles on the fluid, in turn, is considered by imposing consistent boundary conditions on the fluid at its corresponding interfaces with the particles. This is achieved through an immersed boundaries technique. An implicit, staggered, coupled FEM–DEM scheme is developed within a time-marching solution process. Examples of numerical simulations are provided to illustrate the applicability and potentialities of the proposed method.

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Acknowledgements

Ana C. S. Fernandes and Henrique C. Gomes acknowledge support from the Computational Mechanics Laboratory, University of São Paulo, Brazil. Eduardo M. B. Campello acknowledges support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, under the Grants 309748/2015-1 and 307368/2018-1. André S. Müller acknowledges scholarship funding from FAPEMA (Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão), under the Grant BD-02045/19. Paulo M. Pimenta acknowledges support by CNPq, under the Grant 308142/2018-7 and also expresses his acknowledgment to the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stays at the Universities of Duisburg-Essen and Hannover, in Germany, as well as to the French and Brazilian Governments for the Chair CAPES-Sorbonne that made possible his stay at Sorbonne Universités, on a leave from the University of São Paulo.

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  1. Department of Structural and Geotechnical Engineering, University of São Paulo, P.O. Box 61548, São Paulo, SP, 05424-970, Brazil

    Ana C. S. Fernandes, Henrique C. Gomes, Eduardo M. B. Campello, André S. Müller & Paulo M. Pimenta

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  1. Ana C. S. Fernandes
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  2. Henrique C. Gomes
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  3. Eduardo M. B. Campello
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Correspondence to Eduardo M. B. Campello.

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Fernandes, A.C.S., Gomes, H.C., Campello, E.M.B. et al. A coupled FEM–DEM method for the modeling of fluids laden with particles. Comp. Part. Mech. 8, 349–368 (2021). https://doi.org/10.1007/s40571-020-00336-3

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