Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique

Abstract

Fluid particulate flows are common phenomena in nature and industry. Modeling of such flows at micro and macro levels as well establishing relationships between these approaches are needed to understand properties of the particulate matter. We propose a computational technique based on the direct numerical simulation of the particulate flows. The numerical method is based on the distributed Lagrange multiplier technique following the ideas of Glowinski et al. (1999). Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. Mutual forces for the fluid-particle interactions are internal to the system. Particles interact with the fluid via fluid dynamic equations, resulting in implicit fluid-rigid-body coupling relations that produce realistic fluid flow around the particles (i.e., no-slip boundary conditions). The particle-particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method of Cundall et al. (1979) with some modifications using a volume of an overlapping region as an input to the contact forces. The method is flexible enough to handle arbitrary particle shapes and size distributions. A parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library, which allows handling of large amounts of rigid particles and enables local grid refinement. Accuracy and convergence of the presented method has been tested against known solutions for a falling sphere as well as by examining fluid flows through stationary particle beds (periodic and cubic packing). To evaluate code performance and validate particle contact physics algorithm, we performed simulations of a representative experiment conducted at the University of California at Berkley for pebble flow through a narrow opening.

Application of parallel distributed Lagrange multiplier technique to simulate coupled Fluid-Granular flows in pipes with varying Cross-Sectional area

“…Each particle is treated as an individual grain and it is explicitly resolved on the Eulerian grid using solid volume fractions. The grain cell size in our method is smaller than the particle diameter (see [6]). The fluid equations are solved throughout the entire computational domain; however, Lagrange multiplier constraints are applied inside the particle domain, such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body.…”

“…In this paper we generalize analytical findings and complement them by numerical results and experimental data. In order to analyze and quantify such fluid-granular flows, we perform direct numerical simulations using the distributed Lagrange multiplier technique (Glowinski et al, 1999, Patankar, 2001, Kanarska et al, 2011) and compare them with experiment conducted at Lawrence Livermore National Laboratory. A systematic variation of the flow and particle parameters is part of an on-going simulation study of fluid-solid granular flows through relatively small pipes.…”

Evolution of an interfacial crack on the concrete-embankment boundary

“…The results of comparison against Ergun equation for flow through stationary beds (periodic and cubic packing) can be found in Kanarska et al (2011).…”

“…Here we attempt to clarify these uncertainties with the help of numerical experiments using the grain-scale model (Kanarska et al 2011). First, we establish a set of particle-scale configurations to study response of a granular bed to forcing by a fluid which flows over the crack surface for different particle sizes, shapes, and environmental conditions.…”

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

“…Using the DLM, Pan et al [23] simulated the behaviour of fluidized beds; however, they ignored particle-particle interactions to keep the computational costs low. More recently, Kanarska et al [24] have coupled the DLM with the DEM for particle-particle interactions. Fully resolved simulations of particle-laden flows using FD by Avci & Wriggers [3] is in spirit similar to the DLM, except that coupling forces are computed by integrating the stress field at the surface of the particles.…”