Eulerian-Lagrangian and Eulerian-Eulerian approaches for the simulation of particle-laden free surface flows using the lattice Boltzmann method

Abstract This paper studies the Eulerian–Lagrangian and Eulerian–Eulerian approaches for the simulation of interaction between free surface flow and particles. The dynamics of the fluid as well as the transport of the particles in the Eulerian description is solved using the lattice Boltzmann method. To minimize artificial diffusion in particle transport the lattice Boltzmann method with direction-dependent stabilization is proposed. The interaction between the fluid and particles is ensured using the particulate immersed boundary method, where the two-ways coupling algorithm is considered. The developed Eulerian–Lagrangian and Eulerian–Eulerian schemes are compared with each other and validated against results from literature. Both schemes are applied to free surfaces flow problems with complex geometries similar to real gravity casting problems with fillers.

[1]  Jie Ouyang,et al.  Lattice Boltzmann model for the volume-averaged Navier-Stokes equations , 2014, 1406.6438.

[2]  Y. J. Zhang,et al.  Simulation of casting filling process using the lattice Boltzmann method , 2019, IOP Conference Series: Materials Science and Engineering.

[3]  Kyung Chun Kim,et al.  Lattice Boltzmann simulation of solid particles behavior in a three-dimensional lid-driven cavity flow , 2014, Comput. Math. Appl..

[4]  Manfred Krafczyk,et al.  Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios , 2014 .

[5]  Shiyi Chen,et al.  Stability Analysis of Lattice Boltzmann Methods , 1993, comp-gas/9306001.

[6]  Zhaoxia Yang,et al.  Convergence of lattice Boltzmann methods for Navier–Stokes flows in periodic and bounded domains , 2009, Numerische Mathematik.

[7]  F. Xavier Trias,et al.  PIBM: Particulate immersed boundary method for fluid–particle interaction problems , 2014, 1407.6704.

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

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

[10]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  Yang Hu,et al.  An improved momentum exchanged-based immersed boundary-lattice Boltzmann method by using an iterative technique , 2014, Comput. Math. Appl..

[12]  M. Passandideh-Fard,et al.  A two-phase lattice Boltzmann study on injection filling of cavities with arbitrary shapes , 2017 .

[13]  Olivier Simonin,et al.  Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence , 2008, J. Comput. Phys..

[14]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[15]  K. W. Lee,et al.  Theoretical Study of Aerosol Filtration by Fibrous Filters , 1982 .

[16]  Mathias J. Krause,et al.  Multiscale Simulation with a Two‐Way Coupled Lattice Boltzmann Method and Discrete Element Method , 2017 .

[17]  P. Malinowski,et al.  Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry , 2017 .

[18]  Volker John,et al.  An assessment of discretizations for convection-dominated convection–diffusion equations , 2011 .

[19]  Willy Dörfler,et al.  Inertial dilute particulate fluid flow simulations with an Euler-Euler lattice Boltzmann method , 2016, J. Comput. Sci..

[20]  Z. Feng,et al.  The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems , 2004 .

[21]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  ChuiJie Wu,et al.  Particle sedimentation using hybrid Lattice Boltzmann-immersed boundary method scheme , 2017 .

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

[24]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Konrad Steiner,et al.  Lattice Boltzmann model for free-surface flow and its application to filling process in casting , 2003 .

[26]  John W. Crawford,et al.  A novel three‐dimensional lattice Boltzmann model for solute transport in variably saturated porous media , 2002 .

[27]  Chen,et al.  Lattice Boltzmann thermohydrodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Volker John,et al.  On Finite Element Methods for 3D Time-Dependent Convection-Diffusion-Reaction Equations with Small Diffusion , 2008 .

[30]  Mohammad Faghri,et al.  Computer Modeling of Aerosol Filtration by Fibrous Filters , 1988 .

[31]  Raffaele Tripiccione,et al.  Massively parallel lattice-Boltzmann codes on large GPU clusters , 2016, Parallel Comput..

[32]  P. Neofytou,et al.  A fully Eulerian approach to particle inertial deposition in a physiologically realistic bifurcation , 2013 .

[33]  J. Vimmr,et al.  Numerical and experimental prediction of free surface flow of shear-thinning fluids , 2021, Computers & Fluids.

[34]  Willy Dörfler,et al.  Parallel dilute particulate flow simulations in the human nasal cavity , 2016 .

[35]  Nils Thürey,et al.  Physically based animation of free surface flows with the Lattice Boltzmann method , 2007 .

[36]  J. Koelman,et al.  A Simple Lattice Boltzmann Scheme for Navier-Stokes Fluid Flow , 1991 .

[37]  Chang Shu,et al.  TAYLOR SERIES EXPANSION AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD: THREE-DIMENSIONAL FORMULATION AND ITS APPLICATIONS , 2003 .

[38]  Akiyama,et al.  Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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