Finite element methods for particle-laden flows

(English) In this monograph, we develop a numerical method to model dense particle-laden flows. We analyze the key components of a particle-laden flow algorithm, which are the stabilization of the fluid formulation, the modeling of the dispersed phase by means of the point-particle approach, and the...

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Detalles Bibliográficos
Autor: González Usúa, Joaquín
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:CBUC, CESCA
Repositorio:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/694373
Acceso en línea:http://hdl.handle.net/10803/694373
https://dx.doi.org/10.5821/dissertation-2117-428815
Access Level:acceso embargado
Palabra clave:Finite Element
Eulerian-Lagrangian coupling
Variational Multiscale
Volume Averaged Navier-Stokes
Ensemble Averaged Navier-Stokes
Particle-laden flows
Àrees temàtiques de la UPC::Enginyeria mecànica
Àrees temàtiques de la UPC::Matemàtiques i estadística
531/534 - Mecànica. Vibracions. Acústica
51 - Matemàtiques
Descripción
Sumario:(English) In this monograph, we develop a numerical method to model dense particle-laden flows. We analyze the key components of a particle-laden flow algorithm, which are the stabilization of the fluid formulation, the modeling of the dispersed phase by means of the point-particle approach, and the design of the unresolved coupling between phases based on the physical theory. The first part covers the development of a finite element method for the Navier-Stokes equations applicable to inertial porous media flows. We use the Variational Multiscale framework to develop a stabilized formulation that allows to use finite element spaces with equal-order interpolation for the unknowns, and prevent the instabilities that arise for convection-dominated or reaction-dominated flows. In the second part, we extend the stabilized formulation to the transient averaged porous NavierStokes equations. Two different formulations are compared in a set of numerical simulations aimed at evaluating their stability in time and space for a given time-dependent fluid fraction field. The final part focuses on developing an effective coupling strategy between the particles and the fluid phases. We describe a kernel-based method to coarse-grain the discrete variables that allows a decoupling between the kernel shape and size, and the discretization mesh. We show that our strategy conserves mass, linear, and angular momenta, which we analyze via numerical tests. Finally, we apply our method to two examples from the literature to showcase that our Eulerian-Lagrangian algorithm can perform well with dense gas-solid and liquid-solid systems.