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Ginzburg I, Silva G, Marson F, Chopard B, Latt J. Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows. Phys Rev E 2023; 107:025303. [PMID: 36932550 DOI: 10.1103/physreve.107.025303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 01/08/2023] [Indexed: 02/11/2023]
Abstract
The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with two infinite-member boundary classes: (1) the single-node "Linear Plus" (LI^{+}) and (2) the two-node "Extended Multireflection" (EMR). The LI^{+} unifies all directional rules relying on the linear combinations of up to three pre- or postcollision populations, including their "ghost-node" interpolations and adjustable nonequilibrium approximations. On this basis, we propose three groups of LI^{+} nonequilibrium local corrections: (1) the LI_{1}^{+} is parametrized, meaning that its steady-state solution is physically consistent: the momentum accuracy is viscosity-independent in Stokes flow, and it is fixed by the Reynolds number (Re) in inertial flow; (2) the LI_{3}^{+} is parametrized, exact for arbitrary grid-rotated Poiseuille force-driven Stokes flow and thus most accurate in porous flow; and (3) the LI_{4}^{+} is parametrized, exact for pressure and inertial term gradients, and hence advantageous in very narrow porous gaps and at higher Reynolds range. The directional, two-relaxation-time collision operator plays a crucial role for all these features, but also for efficiency and robustness of the boundary schemes due to a proposed nonequilibrium linear stability criterion which reliably delineates their suitable coefficients and relaxation space. Our methodology allows one to improve any directional rule for Stokes or Navier-Stokes accuracy, but their parametrization is not guaranteed. In this context, the parametrized two-node EMR class enlarges the single-node schemes to match exactness in a grid-rotated linear Couette flow modeled with an equilibrium distribution designed for the Navier-Stokes equation (NSE). However, exactness of a grid-rotated Poiseuille NSE flow requires us to perform (1) the modification of the standard NSE term for exact bulk solvability and (2) the EMR extension towards the third neighbor node. A unique relaxation and equilibrium exact configuration for grid-rotated Poiseuille NSE flow allows us to classify the Galilean invariance characteristics of the boundary schemes without any bulk interference; in turn, its truncated solution suggests how, when increasing the Reynolds number, to avoid a deterioration of the mass-leakage rate and momentum accuracy due to a specific Reynolds scaling of the kinetic relaxation collision rate. The optimal schemes and strategies for creeping and inertial regimes are then singled out through a series of numerical tests, such as grid-rotated channels and rotated Couette flow with wall-normal injection, cylindrical porous array, and Couette flow between concentric cylinders, also comparing them against circular-shape fitted FEM solutions.
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Affiliation(s)
- Irina Ginzburg
- Université Paris-Saclay, INRAE, UR HYCAR, 92160 Antony, France
| | - Goncalo Silva
- IDMEC, University of Évora, 7000-671 Évora, Portugal
| | | | | | - Jonas Latt
- University of Geneva, 1204 Geneva, Switzerland
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Marson F, Thorimbert Y, Chopard B, Ginzburg I, Latt J. Enhanced single-node lattice Boltzmann boundary condition for fluid flows. Phys Rev E 2021; 103:053308. [PMID: 34134275 DOI: 10.1103/physreve.103.053308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 03/29/2021] [Indexed: 11/07/2022]
Abstract
We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations. The second is to enhance them by limiting the interpolation extension to the proximity of the boundary. Despite its local nature, the resulting method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well-established Bouzidi's scheme for curved walls [M. Bouzidi, M. Firdaouss, and P. Lallemand, Phys. Fluids 13, 3452 (2001)]PHFLE61070-663110.1063/1.1399290. Among the infinite number of possibilities, we identify several meaningful variants of the method, discerned by their approximation of the second-order nonequilibrium terms and their interpolation coefficients. For each one, we provide two parametrized versions that produce viscosity independent accuracy at steady state. The method proves to be suitable to simulate moving rigid objects or surfaces moving following either the rigid body dynamics or a prescribed kinematic. Also, it applies uniformly and without modifications in the whole domain for any shape, including corners, narrow gaps, or any other singular geometry.
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Affiliation(s)
- Francesco Marson
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - Yann Thorimbert
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - Bastien Chopard
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - Irina Ginzburg
- Paris-Saclay University, INRAE, UR HYCAR, 92160, Antony, France
| | - Jonas Latt
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
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Fitzgerald BW, Zarghami A, Mahajan VV, Sanjeevi SK, Mema I, Verma V, El Hasadi YM, Padding JT. Multiscale simulation of elongated particles in fluidised beds. CHEMICAL ENGINEERING SCIENCE: X 2019. [DOI: 10.1016/j.cesx.2019.100019] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Sanjeevi SKP, Zarghami A, Padding JT. Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows. Phys Rev E 2018; 97:043305. [PMID: 29758688 DOI: 10.1103/physreve.97.043305] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2017] [Indexed: 11/07/2022]
Abstract
Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.
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Affiliation(s)
- Sathish K P Sanjeevi
- Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Ahad Zarghami
- Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Johan T Padding
- Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
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Jäger R, Mendoza M, Herrmann HJ. Channelization in porous media driven by erosion and deposition. Phys Rev E 2017; 95:013110. [PMID: 28208459 DOI: 10.1103/physreve.95.013110] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2016] [Indexed: 06/06/2023]
Abstract
We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Furthermore we investigate how changes of the local deposition and erosion properties affect the final state of the porous structure, finding that the larger the range of wall shear stress for which there is neither erosion nor deposition, the more steady channels are formed in the structure.
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Affiliation(s)
- R Jäger
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
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Chen Q, Zhang X, Zhang J. Improved treatments for general boundary conditions in the lattice Boltzmann method for convection-diffusion and heat transfer processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:033304. [PMID: 24125382 DOI: 10.1103/physreve.88.033304] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2013] [Revised: 08/09/2013] [Indexed: 06/02/2023]
Abstract
In spite of the increasing applications of the lattice Boltzmann method (LBM) in simulating various flow and transport systems in recent years, complex boundary conditions for the convection-diffusion and heat transfer processes in LBM have not been well addressed. In this paper, we propose an improved bounce-back method by using the midpoint concentration value to modify the bounced-back density distribution for LBM simulations of the concentration field. An accurate finite-difference scheme in the normal boundary direction has also been introduced for gradient boundary conditions. Compared with existing boundary methods, our method has a simple algorithm and can easily deal with boundaries with general geometries, motions, and surface conditions (the Dirichlet, Neumann, and mixed conditions). Carefully designed simulations are performed to examine the capacity and accuracy of this proposed boundary method. Simulation results are compared with those from theory and a representative boundary method, and an improved performance is observed. We have also simulated the effect of reference velocity on global accuracy to examine the performance of our model in preserving the fundamental Galilean invariance. These boundary treatments for concentration boundary conditions can be readily applied to other processes such as heat transfer systems.
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Affiliation(s)
- Qing Chen
- School of Energy and Power Engineering, Nanjing University of Science and Technology, Jiangsu 210094, China and Bharti School of Engineering, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada
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Chen Y, Cai Q, Xia Z, Wang M, Chen S. Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:013303. [PMID: 23944579 DOI: 10.1103/physreve.88.013303] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2013] [Indexed: 06/02/2023]
Abstract
The momentum exchange method has been widely used in lattice Boltzmann simulations for particle-fluid interactions. Although proved accurate for still walls, it will result in inaccurate particle dynamics without corrections. In this work, we reveal the physical cause of this problem and find that the initial momentum of the net mass transfer through boundaries in the moving-boundary treatment is not counted in the conventional momentum exchange method. A corrected momentum exchange method is then proposed by taking into account the initial momentum of the net mass transfer at each time step. The method is easy to implement with negligible extra computation cost. Direct numerical simulations of a single elliptical particle sedimentation are carried out to evaluate the accuracy for our method as well as other lattice Boltzmann-based methods by comparisons with the results of the finite element method. A shear flow test shows that our method is Galilean invariant.
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Affiliation(s)
- Yu Chen
- Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China
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