A comprehensive parametric study of LBM-DEM for immersed granular flows

Abstract This paper presents a parametric study of a fluid-particle model which couples Lattice Boltzmann Method (LBM) and Discrete Element Method (DEM) using an immersed moving boundary technique. Benchmark cases with increasing complexity are simulated to understand the numerical accuracy, stability and efficiency of the algorithm. A guideline for a high-quality LBM-DEM model is proposed and applied to a test case of granular collapse in water. The simulation result shows excellent agreement with a companion experiment, which demonstrates the capability of LBM-DEM to describe the dynamics of densely packed and friction dominant immersed granular flows, highlighting its potential to study geophysical mass movements.

[1]  Luc Sibille,et al.  Modeling of fluid–solid interaction in granular media with coupled lattice Boltzmann/discrete element methods: application to piping erosion , 2013 .

[2]  D. Clague,et al.  The hydrodynamic force and torque on a bounded sphere in Poiseuille flow , 2001 .

[3]  Y. T. Feng,et al.  A novel algorithm of immersed moving boundary scheme for fluid–particle interactions in DEM–LBM , 2019, Computer Methods in Applied Mechanics and Engineering.

[4]  F. Maio,et al.  Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes , 2004 .

[5]  Robert K. Niven,et al.  Physical insight into the Ergun and Wen & Yu equations for fluid flow in packed and fluidised beds , 2002 .

[6]  C. Aidun,et al.  Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation , 1998, Journal of Fluid Mechanics.

[7]  Chung Yee Kwok,et al.  Extended CFD–DEM for free‐surface flow with multi‐size granules , 2016 .

[8]  Ulrich Rüde,et al.  A Coupled Lattice Boltzmann Method and Discrete Element Method for Discrete Particle Simulations of Particulate Flows , 2017, Computers & Fluids.

[9]  Y. Feng,et al.  Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues , 2007 .

[10]  Ahmet H. Aydilek,et al.  Laboratory validation of lattice Boltzmann method for modeling pore-scale flow in granular materials , 2006 .

[11]  S. Whitaker Flow in porous media I: A theoretical derivation of Darcy's law , 1986 .

[12]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[13]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[14]  B. Cook,et al.  Three‐dimensional immersed boundary conditions for moving solids in the lattice‐Boltzmann method , 2007 .

[15]  C. Kloss,et al.  Models, algorithms and validation for opensource DEM and CFD-DEM , 2012 .

[16]  D. R. J. Owen,et al.  Numerical Simulations of Irregular Particle Transport in Turbulent Flows Using Coupled LBM-DEM , 2007 .

[17]  P. A. Cundall,et al.  Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method , 2011 .

[18]  S. Ergun Fluid flow through packed columns , 1952 .

[19]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[20]  Jos Derksen,et al.  Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity , 2002 .

[21]  P. A. Cundall,et al.  LBM–DEM modeling of fluid–solid interaction in porous media , 2013 .

[22]  Y. Feng,et al.  Numerical modelling of fluid-induced soil erosion in granular filters using a coupled bonded particle lattice Boltzmann method , 2017 .

[23]  David R. Owen,et al.  Combined three‐dimensional lattice Boltzmann method and discrete element method for modelling fluid–particle interactions with experimental assessment , 2010 .

[24]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[25]  Chong Peng,et al.  Dilatancy and compaction effects on the submerged granular column collapse , 2017 .

[26]  Yan Peng,et al.  Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  C. Peskin The immersed boundary method , 2002, Acta Numerica.

[28]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

[29]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[30]  J. Bray,et al.  Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme , 2004 .

[31]  F. Radjaï,et al.  Collapse dynamics and runout of dense granular materials in a fluid. , 2012, Physical review letters.

[32]  D. Brien,et al.  Acute sensitivity of landslide rates to initial soil porosity. , 2000, Science.

[33]  Qisu Zou,et al.  N ov 1 99 6 On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model , 2008 .

[34]  Cheng Cheng,et al.  An improved immersed moving boundary for the coupled discrete element lattice Boltzmann method , 2018, Computers & Fluids.

[35]  Jungwoo Kim,et al.  An immersed-boundary finite-volume method for simulations of flow in complex geometries , 2001 .

[36]  Shiyi Chen,et al.  A Lattice Boltzmann Subgrid Model for High Reynolds Number Flows , 1994, comp-gas/9401004.

[37]  Wei Shyy,et al.  Lattice Boltzmann Method for 3-D Flows with Curved Boundary , 2000 .

[38]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[39]  G. N. Pande,et al.  A coupled 3‐dimensional bonded discrete element and lattice Boltzmann method for fluid‐solid coupling in cohesive geomaterials , 2018, International Journal for Numerical and Analytical Methods in Geomechanics.

[40]  Saiied M. Aminossadati,et al.  Improved coupling of time integration and hydrodynamic interaction in particle suspensions using the lattice Boltzmann and discrete element methods , 2018, Comput. Math. Appl..

[41]  C. Kwok,et al.  Dynamics and scaling laws of underwater granular collapse with varying aspect ratios , 2018, Physical Review E.

[42]  J. R. Torczynski,et al.  A Lattice-Boltzmann Method for Partially Saturated Computational Cells , 1998 .

[43]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[44]  I. F. Macdonald,et al.  Flow through Porous Media-the Ergun Equation Revisited , 1979 .

[45]  M. Mooney,et al.  The viscosity of a concentrated suspension of spherical particles , 1951 .

[46]  Jidong Zhao,et al.  Coupled CFD–DEM simulation of fluid–particle interaction in geomechanics , 2013 .

[47]  Alice,et al.  Parallel Open Source CFD-DEM for Resolved Particle-Fluid Interaction , 2013 .

[48]  Ulrich Rüde,et al.  A comparative study of fluid-particle coupling methods for fully resolved lattice Boltzmann simulations , 2017, ArXiv.

[49]  C. Kwok,et al.  The effects of bed form roughness on total suspended load via the Lattice Boltzmann Method , 2018, Applied Mathematical Modelling.

[50]  David R. Owen,et al.  An efficient framework for fluid–structure interaction using the lattice Boltzmann method and immersed moving boundaries , 2011 .

[51]  L. Verlet Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[52]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[53]  O. Pouliquen,et al.  Granular collapse in a fluid: Role of the initial volume fraction , 2010 .

[54]  E. J. Hinch,et al.  The elastohydrodynamic collision of two spheres , 1986, Journal of Fluid Mechanics.