Mesoscale dynamic coupling of finite- and discrete-element methods for fluid-particle interactions

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 372; no. 2021; p. 20130386
• Main Authors: Srivastava, S., Yazdchi, K., Luding, S.
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 06.08.2014
• Subjects: Delaunay Tessellation; Discrete-Element Method Two-Way Coupling; Finite-Element Method; Multi-Phase Flow; Multi-Scale Methods; Numerical Analysis; discrete-element method two-way coupling; multi-scale methods; Delaunay tessellation; finite-element method; multi-phase flow; numerical analysis
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2013.0386

A new method for two-way fluid-particle coupling on an unstructured mesoscopically coarse mesh is presented. In this approach, we combine a (higher order) finite-element method (FEM) on the moving mesh for the fluid with a soft sphere discrete-element method for the particles. The novel feature of the proposed scheme is that the FEM mesh is a dynamic Delaunay triangulation based on the positions of the moving particles. Thus, the mesh can be multi-purpose: it provides (i) a framework for the discretization of the Navier-Stokes equations, (ii) a simple tool for detecting contacts between moving particles, (iii) a basis for coarse-graining or upscaling, and (iv) coupling with other physical fields (temperature, electromagnetic, etc.). This approach is suitable for a wide range of dilute and dense particulate flows, because the mesh resolution adapts with particle density in a given region. Two-way momentum exchange is implemented using semi-empirical drag laws akin to other popular approaches; for example, the discrete particle method, where a finite-volume solver on a coarser, fixed grid is used. We validate the methodology with several basic test cases, including single- and double-particle settling with analytical and empirical expectations, and flow through ordered and random porous media, when compared against finely resolved FEM simulations of flow through fixed arrays of particles.