Lattice Boltzmann Method for 3-D Flows with Curved Boundary
NASA Technical Reports Server (NTRS)
Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi
2002-01-01
In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.
Multiple-Relaxation-Time Lattice Boltzmann Models in 3D
NASA Technical Reports Server (NTRS)
dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
NASA Astrophysics Data System (ADS)
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
Development and validation of a 3D Lattice Boltzmann model for volcano aeroacoustics
NASA Astrophysics Data System (ADS)
Brogi, Federico; Bonadonna, Costanza; Ripepe, Maurizio; Chopard, Bastien; Malaspinas, Orestis; Latt, Jonas; Falcone, Jean-Luc
2015-04-01
Infrasound measurements have a great potential for the real time characterization of volcanic plume source parameters [Ripepe et al., 2013]. Nonetheless many shortcomings have been highlighted in the understanding of the infrasound monitoring. In particular, the application of the classical acoustic source models to volcanic explosive eruptions has shown to be challenging and a better knowledge of the link between the acoustic radiation and actual volcanic fluid dynamics processes is required. New insights into this subject could be given by the study of realistic aeroacoustic numerical simulations of a volcanic jet. Our work mainly focuses on developing and validating such numerical model to determine when and if classical model source theory can be applied to explain volcanic infrasound data. Lattice Boltzmann strategies (LB) provide the opportunity to develop an accurate, computationally fast, 3D physical model for a volcanic jet and wave propagation. In the field of aeroacoustic applications, dedicated LB schemes has been proven to have the low dispersion and dissipative properties needed for capturing the weak acoustic pressure fluctuations. However, when dealing with simulations of realistic flows, artificial boundaries are defined around the flow region. The reflected waves from these boundaries can have significant influence on the flow field and overwhelm the acoustic field of interest. A special absorbing boundary layer has been implemented in our model to suppress the reflected waves [Xu et al., 2013]. In addition, for highly multi-scale turbulent flows, such as volcanic plumes, the number of grid points needed to represent the smallest scales might become intractable and the most complicated physics happen only in small portions of the computational domain. The implementation of the grid refinement, in our model allow us to insert local finer grids only where is actually needed [Lagrava et al., 2012] and to increase the size of the computational domain
Lattice Boltzmann simulation of dynamics of plunge and pitch of 3D flexible wing
NASA Astrophysics Data System (ADS)
Qi, Dewei; Shyy, Wei
2008-11-01
The method of lattice Boltzmann (LB) simulation has been used to simulate fluid structures and motion of a flexible insect wing in a 3D space. In the method, a beam has been discretized into a chain of rigid segments. Each segment is connected through ball and socket joints at its ends. One segment may be bent and twisted with its neighboring segment. A constraint force is applied to each joint to ensure the solid structure moving as a whole flexible elastic body.We have demonstrated that the LB method is suitable for modeling of aerodynamics of insects flight at low Reynolds numbers. First, a simulation of plunging and pitching of a rigid wing is performed at Re=75 in a 2D space and the results of lift forces and flow structures are in excellent agreement with the previous results. Second, plunging and pitching of a flexible wing in span-wise direction is simulated at Re=136 in a 3D space. We found that when twisting elasticity is large enough the twisting angle could be controlled at a level of smaller than 0.2 degree. It is shown that as bending and twisting elasticity is large enough, the motion of flexible wing approaches that of a rigid membrane wing. The simulation results show that the optimization of flexibility in span-wise direction will benefit thrust and an intermediate level is favorable. The results are consistent with experimental finding.
Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem
Abas, Aizat; Mokhtar, N. Hafizah; Ishak, M. H. H.; Abdullah, M. Z.; Ho Tian, Ang
2016-01-01
This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required. PMID:27239221
Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem.
Abas, Aizat; Mokhtar, N Hafizah; Ishak, M H H; Abdullah, M Z; Ho Tian, Ang
2016-01-01
This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required. PMID:27239221
Dual FIB-SEM 3D imaging and lattice boltzmann modeling of porosimetry and multiphase flow in chalk.
Rinehart, Alex; Petrusak, Robin; Heath, Jason E.; Dewers, Thomas A.; Yoon, Hongkyu
2010-12-01
Mercury intrusion porosimetry (MIP) is an often-applied technique for determining pore throat distributions and seal analysis of fine-grained rocks. Due to closure effects, potential pore collapse, and complex pore network topologies, MIP data interpretation can be ambiguous, and often biased toward smaller pores in the distribution. We apply 3D imaging techniques and lattice-Boltzmann modeling in interpreting MIP data for samples of the Cretaceous Selma Group Chalk. In the Mississippi Interior Salt Basin, the Selma Chalk is the apparent seal for oil and gas fields in the underlying Eutaw Fm., and, where unfractured, the Selma Chalk is one of the regional-scale seals identified by the Southeast Regional Carbon Sequestration Partnership for CO2 injection sites. Dual focused ion - scanning electron beam and laser scanning confocal microscopy methods are used for 3D imaging of nanometer-to-micron scale microcrack and pore distributions in the Selma Chalk. A combination of image analysis software is used to obtain geometric pore body and throat distributions and other topological properties, which are compared to MIP results. 3D data sets of pore-microfracture networks are used in Lattice Boltzmann simulations of drainage (wetting fluid displaced by non-wetting fluid via the Shan-Chen algorithm), which in turn are used to model MIP procedures. Results are used in interpreting MIP results, understanding microfracture-matrix interaction during multiphase flow, and seal analysis for underground CO2 storage.
LBM-EP: Lattice-Boltzmann method for fast cardiac electrophysiology simulation from 3D images.
Rapaka, S; Mansi, T; Georgescu, B; Pop, M; Wright, G A; Kamen, A; Comaniciu, Dorin
2012-01-01
Current treatments of heart rhythm troubles require careful planning and guidance for optimal outcomes. Computational models of cardiac electrophysiology are being proposed for therapy planning but current approaches are either too simplified or too computationally intensive for patient-specific simulations in clinical practice. This paper presents a novel approach, LBM-EP, to solve any type of mono-domain cardiac electrophysiology models at near real-time that is especially tailored for patient-specific simulations. The domain is discretized on a Cartesian grid with a level-set representation of patient's heart geometry, previously estimated from images automatically. The cell model is calculated node-wise, while the transmembrane potential is diffused using Lattice-Boltzmann method within the domain defined by the level-set. Experiments on synthetic cases, on a data set from CESC'10 and on one patient with myocardium scar showed that LBM-EP provides results comparable to an FEM implementation, while being 10 - 45 times faster. Fast, accurate, scalable and requiring no specific meshing, LBM-EP paves the way to efficient and detailed models of cardiac electrophysiology for therapy planning. PMID:23286029
Dual FIB-SEM 3D Imaging and Lattice Boltzmann Modeling of Porosimetry and Multiphase Flow in Chalk
NASA Astrophysics Data System (ADS)
Rinehart, A. J.; Yoon, H.; Dewers, T. A.; Heath, J. E.; Petrusak, R.
2010-12-01
Mercury intrusion porosimetry (MIP) is an often-applied technique for determining pore throat distributions and seal analysis of fine-grained rocks. Due to closure effects, potential pore collapse, and complex pore network topologies, MIP data interpretation can be ambiguous, and often biased toward smaller pores in the distribution. We apply 3D imaging techniques and lattice-Boltzmann modeling in interpreting MIP data for samples of the Cretaceous Selma Group Chalk. In the Mississippi Interior Salt Basin, the Selma Chalk is the apparent seal for oil and gas fields in the underlying Eutaw Fm., and, where unfractured, the Selma Chalk is one of the regional-scale seals identified by the Southeast Regional Carbon Sequestration Partnership for CO2 injection sites. Dual focused ion - scanning electron beam and laser scanning confocal microscopy methods are used for 3D imaging of nanometer-to-micron scale microcrack and pore distributions in the Selma Chalk. A combination of image analysis software is used to obtain geometric pore body and throat distributions and other topological properties, which are compared to MIP results. 3D data sets of pore-microfracture networks are used in Lattice Boltzmann simulations of drainage (wetting fluid displaced by non-wetting fluid via the Shan-Chen algorithm), which in turn are used to model MIP procedures. Results are used in interpreting MIP results, understanding microfracture-matrix interaction during multiphase flow, and seal analysis for underground CO2 storage. This work was supported by the US Department of Energy, Office of Basic Energy Sciences as part of an Energy Frontier Research Center. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Lattice Boltzmann Stokesian dynamics.
Ding, E J
2015-11-01
Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape. PMID:26651812
Lattice Boltzmann Stokesian dynamics
NASA Astrophysics Data System (ADS)
Ding, E. J.
2015-11-01
Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.
NASA Astrophysics Data System (ADS)
Kajzer, A.; Pozorski, J.; Szewc, K.
2014-08-01
In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.
Lattice Boltzmann morphodynamic model
NASA Astrophysics Data System (ADS)
Zhou, Jian Guo
2014-08-01
Morphological change due to sediment transport is a common natural phenomenon in real flows. It involves complex processes of erosion and deposition such as those along beaches and in river beds, imposing a strong strain on human beings. Studying and understanding morphodynamic evolution are essential to protect living environment. Although there are conventional numerical methods like finite difference method and finite volume method for forecast of morphological change by solving flow and morphodynamic equations, the methods are too complex/inefficient to be applied to a real large scale problem. To overcome this, a lattice Boltzmann method is developed to simulate morphological evolution under flows. It provides an alternative way of studying morphodynamics at the full advantages of the lattice Boltzmann methodology. The model is verified by applications to the evolution of one and two dimensional sand dunes under shallow water flows.
NASA Astrophysics Data System (ADS)
Paradis, Hedvig; Andersson, Martin; Sundén, Bengt
2015-09-01
A 3D model at microscale by the lattice Boltzmann method (LBM) is proposed for part of an anode of a solid oxide fuel cell (SOFC) to analyze the interaction between the transport and reaction processes and structural parameters. The equations of charge, momentum, heat and mass transport are simulated in the model. The modeling geometry is created with randomly placed spheres to resemble the part of the anode structure close to the electrolyte. The electrochemical reaction processes are captured at specific sites where spheres representing Ni and YSZ materials are present with void space. This work focuses on analyzing the effect of structural parameters such as porosity, and percentage of active reaction sites on the ionic current density and concentration of H2 using LBM. It is shown that LBM can be used to simulate an SOFC anode at microscale and evaluate the effect of structural parameters on the transport processes to improve the performance of the SOFC anode. It was found that increasing the porosity from 30 to 50 % decreased the ionic current density due to a reduction in the number of reaction sites. Also the consumption of H2 decreased with increasing porosity. When the percentage of active reaction sites was increased while the porosity was kept constant, the ionic current density increased. However, the H2 concentration was slightly reduced when the percentage of active reaction sites was increased. The gas flow tortuosity decreased with increasing porosity.
NASA Astrophysics Data System (ADS)
Paradis, Hedvig; Andersson, Martin; Sundén, Bengt
2016-08-01
A 3D model at microscale by the lattice Boltzmann method (LBM) is proposed for part of an anode of a solid oxide fuel cell (SOFC) to analyze the interaction between the transport and reaction processes and structural parameters. The equations of charge, momentum, heat and mass transport are simulated in the model. The modeling geometry is created with randomly placed spheres to resemble the part of the anode structure close to the electrolyte. The electrochemical reaction processes are captured at specific sites where spheres representing Ni and YSZ materials are present with void space. This work focuses on analyzing the effect of structural parameters such as porosity, and percentage of active reaction sites on the ionic current density and concentration of H2 using LBM. It is shown that LBM can be used to simulate an SOFC anode at microscale and evaluate the effect of structural parameters on the transport processes to improve the performance of the SOFC anode. It was found that increasing the porosity from 30 to 50 % decreased the ionic current density due to a reduction in the number of reaction sites. Also the consumption of H2 decreased with increasing porosity. When the percentage of active reaction sites was increased while the porosity was kept constant, the ionic current density increased. However, the H2 concentration was slightly reduced when the percentage of active reaction sites was increased. The gas flow tortuosity decreased with increasing porosity.
Lattice gas and lattice Boltzmann computational physics
Chen, S.
1993-05-01
Recent developments of the lattice gas automata method and its extension to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and modeling different physics systems. The lattice gas method, regarded as the simplest microscopic and kinetic approach which generates meaningful macroscopic dynamics, is fully parallel and can be easily programmed on parallel machines. In this talk, the author will review basic principles of the lattice gas and lattice Boltzmann method, its mathematical foundation and its numerical implementation. A detailed comparison of the lattice Boltzmann method with the lattice gas technique and other traditional numerical schemes, including the finite-difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows, will be discussed. Recent achievements of the lattice gas and the the lattice Boltzmann method and their applications in surface phenomena, spinodal decomposition and pattern formation in chemical reaction-diffusion systems will be presented.
He, Xiaoyi; Lou, Li-Shi Lou, Li-Shi
1997-12-01
In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. {copyright} {ital 1997} {ital The American Physical Society}
Crystallographic Lattice Boltzmann Method.
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Crystallographic Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-06-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.
Fully relativistic lattice Boltzmann algorithm
Romatschke, P.; Mendoza, M.; Succi, S.
2011-09-15
Starting from the Maxwell-Juettner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm is validated through simulations of a quark-gluon plasma, yielding excellent agreement with hydrodynamic simulations. The present scheme opens the possibility of transferring the recognized computational advantages of lattice kinetic theory to the context of both weakly and ultrarelativistic systems.
Lattice Boltzmann methods in Geosciences
NASA Astrophysics Data System (ADS)
Huber, Christian; Parmigiani, Andrea; Su, Yanqing
2014-05-01
Numerical models often offer the only possible approach to study the complex non-linear dynamics of geodynamical processes that are difficult or impossible to scale for laboratory experiments. The development of improved computer resources has allowed the emergence of large-scale parallel computations in Earth Sciences. These resources have lead to an increasing complexity in models where a greater number of adjustable parameters arise. Although the increasing number of free parameters offers a greater flexibility to fit satisfyingly the set of available constraints (e.g. geochemical, structural) it also provides new challenges in terms of the size of the parameter space and non-uniqueness of model solutions. Another significant challenge associated with state-of-the-art models is that their complexity is in general associated with the addition of parameterizations of the unresolved (small) scale processes. This trend calls for the development of complementary high-performance models to constrain the physics at small-scales where mass, momentum and energy exchanges at interfaces between different phases control the dynamics in heterogeneous media. We argue that more attention should be devoted to the development of multiphase numerical modeling at the granular (pore) scale to investigate the dynamical behavior of heterogeneous media and the emergence of feedbacks that influence the response of these media at much greater scales. The lattice Boltzmann method is a paradigm that emerged almost three decades ago. It is based on kinetic theory and follows a bottom-up approach that contrast the top-down strategy of standard methods such as Finite Volumes, FEM and Finite Differences. Lattice Boltzmann is ideally suited to handle the complex dynamics of multiphase systems at small spatial scales and is very efficient for parallel programing. In this presentation, we discuss the development of different lattice Boltzmann models developed in our group over the last years
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation. PMID:16210189
Recent advances in lattice Boltzmann methods
Chen, S.; Doolen, G.D.; He, X.; Nie, X.; Zhang, R.
1998-12-31
In this paper, the authors briefly present the basic principles of lattice Boltzmann method and summarize recent advances of the method, including the application of the lattice Boltzmann method for fluid flows in MEMS and simulation of the multiphase mixing and turbulence.
Lattice Boltzmann modeling of phonon transport
NASA Astrophysics Data System (ADS)
Guo, Yangyu; Wang, Moran
2016-06-01
A novel lattice Boltzmann scheme is proposed for phonon transport based on the phonon Boltzmann equation. Through the Chapman-Enskog expansion, the phonon lattice Boltzmann equation under the gray relaxation time approximation recovers the classical Fourier's law in the diffusive limit. The numerical parameters in the lattice Boltzmann model are therefore rigorously correlated to the bulk material properties. The new scheme does not only eliminate the fictitious phonon speed in the diagonal direction of a square lattice system in the previous lattice Boltzmann models, but also displays very robust performances in predicting both temperature and heat flux distributions consistent with analytical solutions for diverse numerical cases, including steady-state and transient, macroscale and microscale, one-dimensional and multi-dimensional phonon heat transport. This method may provide a powerful numerical tool for deep studies of nonlinear and nonlocal heat transports in nanosystems.
A Lattice Boltzmann Method for Turbomachinery Simulations
NASA Technical Reports Server (NTRS)
Hsu, A. T.; Lopez, I.
2003-01-01
Lattice Boltzmann (LB) Method is a relatively new method for flow simulations. The start point of LB method is statistic mechanics and Boltzmann equation. The LB method tries to set up its model at molecular scale and simulate the flow at macroscopic scale. LBM has been applied to mostly incompressible flows and simple geometry.
Lattice Boltzmann approach for complex nonequilibrium flows.
Montessori, A; Prestininzi, P; La Rocca, M; Succi, S
2015-10-01
We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion. PMID:26565365
Higher Order Thermal Lattice Boltzmann Model
NASA Astrophysics Data System (ADS)
Sorathiya, Shahajhan; Ansumali, Santosh
2013-03-01
Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of Gauss-Hermite quadrature in this regard is well known. Most of the thermal LBM in the past have suffered from instability due to lack of proper H-theorem and accuracy. Motivated from these issues, the present work develops along the two works and and imposes an eighth higher order moment to get correct thermal physics. We show that this can be done by adding just 6 more velocities to D3Q27 model and obtain a ``multi-speed on lattice thermal LBM'' with 33 velocities in 3D and calO (u4) and calO (T4) accurate fieq with a consistent H-theorem and inherent numerical stability. Simulations for Rayleigh-Bernard as well as velocity and temperature slip in micro flows matches with analytical results. Lid driven cavity set up for grid convergence is studied. Finally, a novel data structure is developed for HPC. The authors express their gratitude for computational resources and financial support provide by Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, India.
Entropic lattice Boltzmann model for compressible flows.
Frapolli, N; Chikatamarla, S S; Karlin, I V
2015-12-01
We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets. PMID:26764625
Entropic lattice Boltzmann model for compressible flows
NASA Astrophysics Data System (ADS)
Frapolli, N.; Chikatamarla, S. S.; Karlin, I. V.
2015-12-01
We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets.
Visualization of 3D optical lattices
NASA Astrophysics Data System (ADS)
Lee, Hoseong; Clemens, James
2016-05-01
We describe the visualization of 3D optical lattices based on Sisyphus cooling implemented with open source software. We plot the adiabatic light shift potentials found by diagonalizing the effective Hamiltonian for the light shift operator. Our program incorporates a variety of atomic ground state configurations with total angular momentum ranging from j = 1 / 2 to j = 4 and a variety of laser beam configurations including the two-beam lin ⊥ lin configuration, the four-beam umbrella configuration, and four beams propagating in two orthogonal planes. In addition to visualizing the lattice the program also evaluates lattice parameters such as the oscillation frequency for atoms trapped deep in the wells. The program is intended to help guide experimental implementations of optical lattices.
Lattice Boltzmann model for compressible fluids
NASA Technical Reports Server (NTRS)
Alexander, F. J.; Chen, H.; Chen, S.; Doolen, G. D.
1992-01-01
A lattice Boltzmann model is derived which simulates compressible fluids. By choosing the parameters of the equilibrium distribution appropriately, the sound speed (which may be set arbitrarily low), bulk viscosity, and kinematic viscosity can be selected. This model simulates compressible flows and can include shocks. With a proper rescaling and zero-sound speed, this model simulates Burgers's equation. The viscosity determined by a Chapman-Enskog expansion compares well with that measured form simulations. The exact solutions of Burgers's equation on the unit circle are compared to solutions of lattice Boltzmann model finding reasonable agreement.
Fast Lattice Boltzmann Solver for Relativistic Hydrodynamics
Mendoza, M.; Herrmann, H. J.; Boghosian, B. M.; Succi, S.
2010-07-02
A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.
Connection Between the Lattice Boltzmann Equation and the Beam Scheme
NASA Technical Reports Server (NTRS)
Xu, Kun; Luo, Li-Shi
1999-01-01
In this paper we analyze and compare the lattice Boltzmann equation with the beam scheme in details. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of lattice Boltzmann equation and the beam scheme. Based on our analysis, we propose an improved multi-dimensional beam scheme.
Boundary conditions for free interfaces with the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Bogner, Simon; Ammer, Regina; Rüde, Ulrich
2015-09-01
In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner et al. [27] is shown to be first order accurate. The article presents a new free surface boundary scheme that is suitable for second order accurate simulations based on the LBM. The new method takes into account the free surface position and its orientation with respect to the computational lattice. Numerical experiments confirm the theoretical findings and illustrate the different behavior of the original method and the new method.
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Cao, N.; Chen, S.; Jin, S.; Martinez, D.
1997-01-01
The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}
Stability analysis of lattice Boltzmann methods
Sterling, J.D.; Chen, Shiyi
1996-01-01
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK collision operator. As a result, it is not surprising that numericaI instability of lattice Boltzmann methods have been frequently encountered by researchers. We present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant-density uniform mean flow. The linear stability depends on the following parameters: the distribution of the mass at a site between the different discrete speeds, the BGK relaxation time, the mean velocity, and the wave-number of the perturbations. This parameter space is too large to compute the complete stability characteristics. We report some stability results for a subset of the parameter space for a 7-velocity hexagonal lattice, a 9-velocity square lattice, and a 15-velocity cubic lattice. Results common to all three lattices are (1) the BGK relaxation time {tau} must be greater than 1/2 corresponding to positive shear viscosity, (2) there exists a maximum stable mean velocity for fixed values of theother parameters, and (3) as {tau} is increased from 1/2 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger {tau}.
Structural stability of Lattice Boltzmann schemes
NASA Astrophysics Data System (ADS)
David, Claire; Sagaut, Pierre
2016-02-01
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurrence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to Lattice Boltzmann schemes (David and Sagaut 2011; 2009a,b; David et al. 2007).
Lattice Boltzmann model for wave propagation.
Zhang, Jianying; Yan, Guangwu; Shi, Xiubo
2009-08-01
A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation. PMID:19792280
Lattice Boltzmann model for simulation of magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William
1991-01-01
A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.
Lattice Boltzmann method and channel flow
NASA Astrophysics Data System (ADS)
Stensholt, Sigvat; Mongstad Hope, Sigmund
2016-07-01
Lattice Boltzmann methods are presented at an introductory level with a focus on fairly simple simulations that can be used to test and illustrate the model’s capabilities. Two scenarios are presented. The first is a simple laminar flow in a straight channel driven by a pressure gradient (Poiseuille flow). The second is a more complex, including a wedge where Moffatt vortices may be induced if the wedge is deep enough. Simulations of the Poiseuille flow scenario accurately capture the theoretical velocity profile. The experiment shows the location of the fluid-wall boundary and the effects viscosity has on the velocity and convergence time. The numerical capabilities of the lattice Boltzmann model are tested further by simulating the more complex Moffatt vortex scenario. The method reproduces with high accuracy the theoretical predction that Moffat vortices will not form in a wedge if the vertex angle exceeds 146°. Practical issues limitations of the lattice Boltzmann method are discussed. In particular the accuracy of the bounce-back boundary condition is first order dependent on the grid resolution.
Consistent lattice Boltzmann equations for phase transitions.
Siebert, D N; Philippi, P C; Mattila, K K
2014-11-01
Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling. PMID:25493907
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems. PMID:26986435
Lattice Boltzmann model for numerical relativity
NASA Astrophysics Data System (ADS)
Ilseven, E.; Mendoza, M.
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder. PMID:14754343
Lattice Boltzmann approach to thermal transpiration
Sofonea, Victor
2006-11-15
Diffuse reflection boundary conditions are introduced in a thermal lattice Boltzmann model to allow for variable fluid density and temperature along the walls. The capability of this model to capture the main characteristics of the thermal transpiration phenomenon in a box at nonvanishing Knudsen numbers is demonstrated. The thermal creep velocity is found to be proportional to the temperature gradient imposed at the wall, whereas the accuracy of the simulation results are found to be of first or second order, depending on the numerical scheme.
Lattice-Boltzmann-based Simulations of Diffusiophoresis
NASA Astrophysics Data System (ADS)
Castigliego, Joshua; Kreft Pearce, Jennifer
We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles by their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. This simulation, in particular, was intended to model an oceanic system where the particles of interest were zooplankton, phytoplankton and microplastics. The separation of plankton from the microplastics was achieved.
Thermal lattice Boltzmann method for complex microflows
NASA Astrophysics Data System (ADS)
Yasuoka, Haruka; Kaneda, Masayuki; Suga, Kazuhiko
2016-07-01
A methodology to simulate thermal fields in complex microflow geometries is proposed. For the flow fields, the regularized multiple-relaxation-time lattice Boltzmann method (LBM) is applied coupled with the diffusive-bounce-back boundary condition for wall boundaries. For the thermal fields, the regularized lattice Bhatnagar-Gross-Krook model is applied. For the thermal wall boundary condition, a newly developed boundary condition, which is a mixture of the diffuse scattering and constant temperature conditions, is applied. The proposed set of schemes is validated by reference data in the Fourier flows and square cylinder flows confined in a microchannel. The obtained results confirm that it is essential to apply the regularization to the thermal LBM for avoiding kinked temperature profiles in complex thermal flows. The proposed wall boundary condition is successful to obtain thermal jumps at the walls with good accuracy.
Multi-Species Thermal Lattice Boltzmann Models
NASA Astrophysics Data System (ADS)
Wah, Darren; Vahala, George; Vahala, Linda; Pavlo, Pavol; Carter, Jonathan
1998-11-01
Thermal Lattice Boltzmann models (TLBM) are ideal for simulating nonlinear macroscopic conservation systems because of their inherent parallelizeability (nearly all operations are purely local). The TLBM solves a linear BGK-like kinetic equation so that the standard nonlinear convective terms in the standard fluid codes are now replaced by a simple shift operator (linear advection) at the kinetic level. Here we extend our previous TLBM to handle a two-species system, utilizing the models of Morse (1964),Greene (1973) and Kotelnikov & Montgomery (1997). Each kinetic equation now has 2 BGK-like relaxation terms : the first is due to self-collisions and the other is due to different- species collisions. The relaxation rates used are appropriate for electron-ion collisions. Certain constraints can be imposed on the relaxed distribution functions so that the cross-species momentum and energy evolutions relax at the rate determined from the full nonlinear Boltzmann integral collision operator. Ionization and recombination processes will also be examined. Both hexagonal and octagonal lattices are studied.
Immersed boundary method implemented in lattice Boltzmann GPU code
NASA Astrophysics Data System (ADS)
Devincentis, Brian; Smith, Kevin; Thomas, John
2015-11-01
Lattice Boltzmann is well suited to efficiently utilize the rapidly increasing compute power of GPUs to simulate viscous incompressible flows. Fluid-structure interaction with solids of arbitrarily complex geometry can be modeled in this framework with the immersed boundary method (IBM). In IBM a solid is modeled by its surface which applies a force at the neighboring lattice points. The majority of published IBMs require solving a linear system in order to satisfy the no-slip condition. However, the method presented by Wang et al. (2014) is unique in that it produces equally accurate results without solving a linear system. Furthermore, the algorithm can be applied in a parallel manner over the immersed boundary and is, therefore, well suited for GPUs. Here, a 2D and 3D version of their algorithm is implemented in Sailfish CFD, a GPU-based open source lattice Boltzmann code. One issue unaddressed by most published work is how to correct force and torque calculated from IBM for translating and rotating solids. These corrections are necessary because the fluid inside the solid affects its inertia in a non-trivial manner. Therefore, this implementation uses the Lagrangian points approximation correction shown by Suzuki and Inamuro (2011) to be accurate.
Thermal equation of state for lattice Boltzmann gases
NASA Astrophysics Data System (ADS)
Ran, Zheng
2009-06-01
The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.
Lattice-Boltzmann Simulation of Tablet Disintegration
NASA Astrophysics Data System (ADS)
Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip
Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.
Lattice Boltzmann simulations of lymphatic pumping
NASA Astrophysics Data System (ADS)
Kunert, Christian; Padera, Tim P.; Munn, Lance L.
2012-02-01
Lymphatic flow plays an important role in the progress of many diseases, including lymphedema and metastasis. However lymphatic pumping and flow is poorly understood. Here, we present a computer model that is based on biological observations of lymphatic pumping. Fluid flow is simulated by a D2Q9 lattice Boltzmann model. The boundary of the vessels moves according to shear-induced nitric oxide production, and wall motion transfers momentum to the fluid to induce flow. Because the model only includes local properties, it can be highly parallelized. In our case we utilize graphic processors (GPU) to achieve high performance computation. We show that the model provides stable pumping over a wide range of parameter values, with optimum flow achieved in the biological ranges. Furthermore, we investigate the efficiency by analyzing the flow rate and pumping frequency in order to compare the behavior of the model with existing in vivo data.
Lattice Boltzmann formulation for Braginskii magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Dellar, Paul
2012-03-01
We present a lattice Boltzmann formulation of the Braginskii magnetohydrodynamic equations that describe large-scale motions in strongly magnetised plasmas. Fluid quantities, density, velocity and stress, are represented by a finite set of distribution functions associated with particles moving on a square or cubic lattice. Equilibrium distributions are constructed from Hermite moment expansions, so slowly varying solutions of the discrete kinetic equation exactly satisfy the Navier--Stokes or MHD momentum equations. Electromagnetic quantities are represented by a second kinetic equation for a set of vector-valued distribution functions. Maxwell's equations and the resistive MHD induction equation may be recovered from slowly varying solutions using different scalings. The resulting algorithm, comprising only local operations at grid points and data copying between adjacent points, readily lends itself to large-scale parallel computations. We modify the collision operator to apply different relaxation times to components of the stress parallel and perpendicular to the local magnetic field, simulating a form of the Braginskii MHD equations encountered in astrophysics. Large shears develop in simulations where the fluid velocity perpendicular to the field lines reverses.
Modeling adsorption with lattice Boltzmann equation
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-01-01
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325
Modeling adsorption with lattice Boltzmann equation.
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-01-01
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325
Convection in Multiphase Fluid Flows Using Lattice Boltzmann Methods
NASA Astrophysics Data System (ADS)
Biferale, L.; Perlekar, P.; Sbragaglia, M.; Toschi, F.
2012-03-01
We present high-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method. We first study the thermodynamical and kinematic properties of the algorithm. Then, we perform a series of 3D numerical simulations changing the mean properties in the phase diagram and compare convection with and without phase coexistence at Rayleigh number Ra˜107. We show that in the presence of nucleating bubbles non-Oberbeck-Boussinesq effects develop, the mean temperature profile becomes asymmetric, and heat-transfer and heat-transfer fluctuations are enhanced, at all Ra studied. We also show that small-scale properties of velocity and temperature fields are strongly affected by the presence of the buoyant bubble leading to high non-Gaussian profiles in the bulk.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere. PMID:26382548
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Lattice Boltzmann algorithm for continuum multicomponent flow.
Halliday, I; Hollis, A P; Care, C M
2007-08-01
We present a multicomponent lattice Boltzmann simulation for continuum fluid mechanics, paying particular attention to the component segregation part of the underlying algorithm. In the principal result of this paper, the dynamics of a component index, or phase field, is obtained for a segregation method after U. D'Ortona [Phys. Rev. E 51, 3718 (1995)], due to Latva-Kokko and Rothman [Phys. Rev. E 71 056702 (2005)]. The said dynamics accord with a simulation designed to address multicomponent flow in the continuum approximation and underwrite improved simulation performance in two main ways: (i) by reducing the interfacial microcurrent activity considerably and (ii) by facilitating simulational access to regimes of flow with a low capillary number and drop Reynolds number [I. Halliday, R. Law, C. M. Care, and A. Hollis, Phys. Rev. E 73, 056708 (2006)]. The component segregation method studied, used in conjunction with Lishchuk's method [S. V. Lishchuk, C. M. Care, and I. Halliday, Phys. Rev. E 67, 036701 (2003)], produces an interface, which is distributed in terms of its component index; however, the hydrodynamic boundary conditions which emerge are shown to support the notion of a sharp, unstructured, continuum interface. PMID:17930175
Lattice Boltzmann Simulations of Peristaltic Particle Transport
NASA Astrophysics Data System (ADS)
Connington, Kevin; Kang, Qinjun; Viswanathan, Hari; Chen, Shiyi; Abdel-Fattah, Amr
2008-11-01
A peristaltic flow occurs when a tube or channel with flexible walls transports the contained fluid by progressing a series of contraction or expansion waves along the length of those walls. It is a mechanism used to transport fluid and immersed solid particles when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two dimensional channel using the Lattice Boltzmann Method (LBM). We systematically investigate the effect of variation of the relevant non-dimensional parameters of the system on the particle transport. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid ``trapping.'' Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles.
Three-dimensional lattice Boltzmann model for magnetic reconnection
Mendoza, M.; Munoz, J. D.
2008-02-15
We develop a three-dimensional (3D) lattice Boltzmann model that recovers in the continuous limit the two-fluids theory for plasmas, and consequently includes the generalized Ohm's law. The model reproduces the magnetic reconnection process just by giving the right initial equilibrium conditions in the magnetotail, without any assumption on the resistivity in the diffusive region. In this model, the plasma is handled similar to two fluids with an interaction term, each one with distribution functions associated to a cubic lattice with 19 velocities (D3Q19). The electromagnetic fields are considered as a third fluid with an external force on a cubic lattice with 13 velocities (D3Q13). The model can simulate either viscous fluids in the incompressible limit or nonviscous compressible fluids, and successfully reproduces both the Hartmann flow and the magnetic reconnection in the magnetotail. The reconnection rate in the magnetotail obtained with this model lies between R=0.062 and R=0.073, in good agreement with the observations.
Three-dimensional lattice Boltzmann model for magnetic reconnection.
Mendoza, M; Muñoz, J D
2008-02-01
We develop a three-dimensional (3D) lattice Boltzmann model that recovers in the continuous limit the two-fluids theory for plasmas, and consequently includes the generalized Ohm's law. The model reproduces the magnetic reconnection process just by giving the right initial equilibrium conditions in the magnetotail, without any assumption on the resistivity in the diffusive region. In this model, the plasma is handled similar to two fluids with an interaction term, each one with distribution functions associated to a cubic lattice with 19 velocities (D3Q19). The electromagnetic fields are considered as a third fluid with an external force on a cubic lattice with 13 velocities (D3Q13). The model can simulate either viscous fluids in the incompressible limit or nonviscous compressible fluids, and successfully reproduces both the Hartmann flow and the magnetic reconnection in the magnetotail. The reconnection rate in the magnetotail obtained with this model lies between R=0.062 and R=0.073, in good agreement with the observations. PMID:18352154
LUDWIG: A parallel Lattice-Boltzmann code for complex fluids
NASA Astrophysics Data System (ADS)
Desplat, Jean-Christophe; Pagonabarraga, Ignacio; Bladon, Peter
2001-03-01
This paper describes Ludwig, a versatile code for the simulation of Lattice-Boltzmann (LB) models in 3D on cubic lattices. In fact, Ludwig is not a single code, but a set of codes that share certain common routines, such as I/O and communications. If Ludwig is used as intended, a variety of complex fluid models with different equilibrium free energies are simple to code, so that the user may concentrate on the physics of the problem, rather than on parallel computing issues. Thus far, Ludwig's main application has been to symmetric binary fluid mixtures. We first explain the philosophy and structure of Ludwig which is argued to be a very effective way of developing large codes for academic consortia. Next we elaborate on some parallel implementation issues such as parallel I/O, and the use of MPI to achieve full portability and good efficiency on both MPP and SMP systems. Finally, we describe how to implement generic solid boundaries, and look in detail at the particular case of a symmetric binary fluid mixture near a solid wall. We present a novel scheme for the thermodynamically consistent simulation of wetting phenomena, in the presence of static and moving solid boundaries, and check its performance.
RNA folding on the 3D triangular lattice
2009-01-01
Background Difficult problems in structural bioinformatics are often studied in simple exact models to gain insights and to derive general principles. Protein folding, for example, has long been studied in the lattice model. Recently, researchers have also begun to apply the lattice model to the study of RNA folding. Results We present a novel method for predicting RNA secondary structures with pseudoknots: first simulate the folding dynamics of the RNA sequence on the 3D triangular lattice, next extract and select a set of disjoint base pairs from the best lattice conformation found by the folding simulation. Experiments on sequences from PseudoBase show that our prediction method outperforms the HotKnot algorithm of Ren, Rastegari, Condon and Hoos, a leading method for RNA pseudoknot prediction. Our method for RNA secondary structure prediction can be adapted into an efficient reconstruction method that, given an RNA sequence and an associated secondary structure, finds a conformation of the sequence on the 3D triangular lattice that realizes the base pairs in the secondary structure. We implemented a suite of computer programs for the simulation and visualization of RNA folding on the 3D triangular lattice. These programs come with detailed documentation and are accessible from the companion website of this paper at http://www.cs.usu.edu/~mjiang/rna/DeltaIS/. Conclusion Folding simulation on the 3D triangular lattice is effective method for RNA secondary structure prediction and lattice conformation reconstruction. The visualization software for the lattice conformations of RNA structures is a valuable tool for the study of RNA folding and is a great pedagogic device. PMID:19891777
An axisymmetric multiple-relaxation-time lattice Boltzmann scheme
NASA Astrophysics Data System (ADS)
Xie, Wenjun
2015-01-01
A multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme developed for axisymmetric flows recovers the complete continuity and Navier-Stokes equations. This scheme follows the strategy of the standard D2Q9 model by using a single particle distribution function and a simple "collision-streaming" updating rule. The extra terms related to axisymmetry in the macroscopic equations are recovered by adding source terms into the LB equation, which are simple and involve no gradients. The compressible effect retained in the Navier-Stokes equations is recovered by introducing a term related to the reversed transformation matrix for MRT collision operator, so as to produce a correct bulk viscosity, making it suitable for compressible flows with high frequency and low Mach number. The validity of the scheme is demonstrated by testing the Hagen-Poiseuille flow and 3D Womersley flow, as well as the standing acoustic waves in a closed cylindrical chamber. The numerical experiments show desirable stability at low viscosities, enabling to simulate a standing ultrasound field in centimeters space.
NASA Technical Reports Server (NTRS)
Mei, Ren-Wei; Shyy, Wei; Yu, Da-Zhi; Luo, Li-Shi; Rudy, David (Technical Monitor)
2001-01-01
The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is
The Lattice Boltzmann Method applied to neutron transport
Erasmus, B.; Van Heerden, F. A.
2013-07-01
In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)
The lattice Boltzmann method and the problem of turbulence
Djenidi, L.
2015-03-10
This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.
Lattice Boltzmann method for weakly ionized isothermal plasmas
Li Huayu; Ki, Hyungson
2007-12-15
In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values.
Zalzale, M.; McDonald, P.J.
2012-12-15
The lattice Boltzmann method is used to investigate the permeability of microstructures of cement pastes generated using the numerical models CEMHYD3D (Bentz, 1997) and {mu}IC (Bishnoi and Scrivener, 2009). Results are reported as a function of paste water-to-cement ratio and degree of hydration. The permeability decreases with increasing hydration and decreasing water-to-cement ratio in agreement with experiment. However the permeability is larger than the experimental data recorded using beam bending methods (Vichit-Vadakan and Scherer, 2002). Notwithstanding, the lattice Boltzmann results compare favourably with alternate numerical methods of permeability calculation for cement model microstructures. In addition, we show early results for the liquid/vapour capillary adsorption and desorption isotherms in the same model {mu}IC structures. The broad features of the experimental capillary porosity isotherm are reproduced, although further work is required to adequately parameterise the model.
Entropic multirelaxation lattice Boltzmann models for turbulent flows.
Bösch, Fabian; Chikatamarla, Shyam S; Karlin, Ilya V
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows. PMID:26565366
Entropic multirelaxation lattice Boltzmann models for turbulent flows
NASA Astrophysics Data System (ADS)
Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.
Lattice Boltzmann Model for Electronic Structure Simulations
NASA Astrophysics Data System (ADS)
Mendoza, M.; Herrmann, H. J.; Succi, S.
2015-09-01
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. By using a discrete version of this new formalism, the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule were calculated accurately. Here, we discuss the main ideas behind the lattice kinetic approach to electronic structure computations, offer some considerations for prospective extensions, and also show additional numerical results, namely the geometrical configuration of the water molecule.
Lattice Boltzmann method for the Saint-Venant equations
NASA Astrophysics Data System (ADS)
Liu, Haifei; Wang, Hongda; Liu, Shu; Hu, Changwei; Ding, Yu; Zhang, Jie
2015-05-01
The Saint-Venant equations represent the hydrodynamic principles of unsteady flows in open channel network through a set of non-linear partial differential equations. In this paper, a new lattice Boltzmann approach to solving the one-dimensional Saint-Venant equations (LABSVE) is developed, demonstrating the variation of discharge and sectional area with external forces, such as bed slope and bed friction. Our research recovers the Saint-Venant equations through deducing the Chapman-Enskog expansion on the lattice Boltzmann equation, which is a mesoscopic technique, bridging the molecular movement and macroscopic physical variables. It is also a fully explicit process, providing simplicity for programming. The model is verified by three benchmark tests: (i) a one-dimensional subcritical gradient flow; (ii) a dam-break wave flow; (iii) a flood event on the Yongding River. The results showed the accuracy of the proposed method and its good applicability in solving Saint-Venant problems.
Conjugate heat transfer with the entropic lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Pareschi, G.; Frapolli, N.; Chikatamarla, S. S.; Karlin, I. V.
2016-07-01
A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.
Conjugate heat transfer with the entropic lattice Boltzmann method.
Pareschi, G; Frapolli, N; Chikatamarla, S S; Karlin, I V
2016-07-01
A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube. PMID:27575234
Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena
NASA Astrophysics Data System (ADS)
Lin, Chuan-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Li, Ying-Jun
2014-11-01
A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.
Modified lattice Boltzmann method for compressible fluid simulations.
Hinton, F L; Rosenbluth, M N; Wong, S K; Lin-Liu, Y R; Miller, R L
2001-06-01
A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory. PMID:11415085
Lattice Boltzmann method on unstructured grids: further developments.
Ubertini, S; Bella, G; Succi, S
2003-07-01
We discuss further developments of the finite-volume lattice Boltzmann formulation on unstructured grids. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size. A theoretical argument of plausibility for such a property is presented. In addition, a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows. PMID:12935281
Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices.
Dechant, Andreas; Kessler, David A; Barkai, Eli
2015-10-23
We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∝H(x,p)(-1/D), where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution. PMID:26551114
Zhang, Yimeng; Li, Xiong; Samonds, Jason M; Lee, Tai Sing
2016-03-01
Bayesian theory has provided a compelling conceptualization for perceptual inference in the brain. Central to Bayesian inference is the notion of statistical priors. To understand the neural mechanisms of Bayesian inference, we need to understand the neural representation of statistical regularities in the natural environment. In this paper, we investigated empirically how statistical regularities in natural 3D scenes are represented in the functional connectivity of disparity-tuned neurons in the primary visual cortex of primates. We applied a Boltzmann machine model to learn from 3D natural scenes, and found that the units in the model exhibited cooperative and competitive interactions, forming a "disparity association field", analogous to the contour association field. The cooperative and competitive interactions in the disparity association field are consistent with constraints of computational models for stereo matching. In addition, we simulated neurophysiological experiments on the model, and found the results to be consistent with neurophysiological data in terms of the functional connectivity measurements between disparity-tuned neurons in the macaque primary visual cortex. These findings demonstrate that there is a relationship between the functional connectivity observed in the visual cortex and the statistics of natural scenes. They also suggest that the Boltzmann machine can be a viable model for conceptualizing computations in the visual cortex and, as such, can be used to predict neural circuits in the visual cortex from natural scene statistics. PMID:26712581
Three-dimensional lattice Boltzmann model for compressible flows.
Sun, Chenghai; Hsu, Andrew T
2003-07-01
A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade. PMID:12935242
NASA Astrophysics Data System (ADS)
Pingen, Georg
The objective of this work is the development of a formal design approach for fluidic systems, providing conceptually novel design layouts with the provision of only boundary conditions and some basic parameters. The lattice Boltzmann method (LBM) is chosen as a flow model due to its simplicity, inherent use of immersed boundary methods, parallelizability, and general flexibility. Immersed Boundary Methods in the form of a Brinkmann penalization are used to continuously vary the flow from fluid to solid, leading to a material distribution based boundary representation. An analytical adjoint sensitivity analysis is derived for the lattice Boltzmann method, enabling the combination of the lattice Boltzmann method with optimization techniques. This results in the first application of design optimization with the lattice Boltzmann method. In particular, the first LBM topology optimization framework for 2D and 3D problems is developed and validated with numerical design optimization problems for drag and pressure drop minimization. To improve the parallel scalability of the LBM sensitivity analysis and permit the solution of large 2D and 3D problems, iterative solvers are studied and a parallel GMRES Schur Complement method is applied to the solution of the linear adjoint problem in the LBM sensitivity analysis. This leads to improved parallel scalability through reduced memory use and algorithmic speedup. The potential of the developed design approach for fluidic systems is illustrated with the optimization of a 3D dual-objective fixed-geometry valve. The use of a parametric level-set method coupled with the LBM material distribution based topology optimization framework is shown to provide further versatility for design applications. Finally, the use of a penalty formulation of the fluid volume constraint permits the topology optimization of flows at moderate Reynolds numbers for a steady-state pipe bend application. Concluding, this work has led to the development of
McHardy, Christopher; Horneber, Tobias; Rauh, Cornelia
2016-07-25
Based on the kinetic theory of photons, a new lattice Boltzmann method for the simulation of 3D radiation transport is presented. The method was successfully validated with Monte Carlo simulations of radiation transport in optical thick absorbing and non-absorbing turbid media containing either isotropic or anisotropic scatterers. Moreover, for the approximation of Mie-scattering, a new iterative algebraic approach for the discretization of the scattering phase function was developed, ensuring full conservation of energy and asymmetry after discretization. It was found that the main error sources of the method are caused by linearization and ray effects and suggestions for further improvement of the method are made. PMID:27464152
Lattice Boltzmann Equation On a 2D Rectangular Grid
NASA Technical Reports Server (NTRS)
Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.
Lattice Boltzmann method for the fractional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Lattice Boltzmann simulation of chemical dissolution in porous media.
Kang, Qinjun; Zhang, Dongxiao; Chen, Shiyi; He, Xiaoyi
2002-03-01
In this paper, we develop a lattice Boltzmann model for simulating the transport and reaction of fluids in porous media. To simulate such a system, we account for the interaction of forced convection, molecular diffusion, and surface reaction. The problem is complicated by the evolution of the porous media geometry due to chemical reactions, which may significantly and continuously modify the hydrologic properties of the media. The particular application that motivates the present study is acid stimulation, a common technique used to increase production from petroleum reservoirs. This technique involves the injection of acid (e.g., hydrochloric acid, HCl, acetic acid, HAc) into the formation to dissolve minerals comprising the rock. As acid is injected, highly conductive channels or "wormholes" may be formed. The dissolution of carbonate rocks in 0.5M HCl and 0.5M HAc is simulated with the lattice Boltzmann model developed in this study. The dependence of dissolution process and the geometry of the final wormhole pattern on the acid type and the injection rate is studied. The results agree qualitatively with the experimental and theoretical analyses of others and substantiate the previous finding that there exists an optimal injection rate at which the wormhole is formed as well as the number of pore volumes of the injected fluid to break through is minimized. This study also confirms the experimentally observed phenomenon that the optimal injection rate decreases and the corresponding minimized number of pore volumes to break through increases as the acid is changed from HCl to HAc. Simulations suggest that the proposed lattice Boltzmann model may serve as an alternative reliable quantitative approach to study chemical dissolution in porous media. PMID:11909255
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering. PMID:27176431
Accuracy of non-Newtonian Lattice Boltzmann simulations
NASA Astrophysics Data System (ADS)
Conrad, Daniel; Schneider, Andreas; Böhle, Martin
2015-11-01
This work deals with the accuracy of non-Newtonian Lattice Boltzmann simulations. Previous work for Newtonian fluids indicate that, depending on the numerical value of the dimensionless collision frequency Ω, additional artificial viscosity is introduced, which negatively influences the accuracy. Since the non-Newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency, a Ω dependent error EΩ is introduced and its influence on the overall error is investigated. Here, simulations with the SRT and the MRT model are carried out for power-law fluids in order to numerically investigate the accuracy of non-Newtonian Lattice Boltzmann simulations. A goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation Mach number, respectively. For the non-Newtonian case, an error estimate for EΩ in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen-Poiseuille channel flow of non-Newtonian fluids. With the help of the error functional, the prediction of the global error minimum of the velocity field is excellent in regions where the EΩ error is the dominant source of error. With an optimal simulation Mach number, the simulation is about one order of magnitude more accurate. Additionally, for both collision models a detailed study of the convergence behavior of the method in the non-Newtonian case is conducted. The results show that the simulation Mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation Mach number.
A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models
NASA Technical Reports Server (NTRS)
Luo, Li-Shi
1998-01-01
A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.
Lattice Boltzmann Modeling of Thrombosis in Giant Aneurysms
NASA Astrophysics Data System (ADS)
Chopard, B.; Ouared, R.; Ruefenacht, D. A.; Yilmaz, H.
We propose a numerical model of blood flow and blood clotting whose purpose is to describe thrombus formation in cerebral aneurysms. We identify possible mechanisms that can cause occurence of spontaneous thrombosis in unruptured giant intracranial aneurysms. Our main claim is that, under normal conditions, there is a low shear rate threshold below which thrombosis starts and growths. This assumption is supported by several evidences from literature. The proposed mechanisms are incorporated into a Lattice Boltzmann (LB) model for blood flow and platelets adhesion and aggregation. Numerical simulations show that the low shear rate threshold assumption together with aneurysm geometry account well for the observations.
Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm
NASA Astrophysics Data System (ADS)
Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.
2008-07-01
The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.
Derivation of the lattice Boltzmann model for relativistic hydrodynamics
Mendoza, M.; Herrmann, H. J.; Boghosian, B. M.; Succi, S.
2010-11-15
A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010) is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid-dynamic problems, namely, shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast wave on massive interstellar clouds. Close to second-order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time steps, are reported.
Thermodynamic-consistent lattice Boltzmann model for nonideal fluids
NASA Astrophysics Data System (ADS)
Wen, Binghai; Qin, Zhangrong; Zhang, Chaoying; Fang, Haiping
2015-11-01
A lattice Boltzmann model to simulate phase separation and two-phase flow is proposed. The nonideal force in multiphase flow is directly computed from the free energy. Thermodynamic consistency and Galilean invariance are theoretically analyzed and numerically verified. Remarkably, the theoretical simplicity endues the model with the advantages of high efficiency and easy implementation. We also find that it can work well together with various equations of state in order to simulate different kinds of multiphase flows. Importantly, it has a tunable parameter κ, which can be used to reduce the effect of spurious current and adjust the surface tension to meet the requirements of researches.
An implicit Lagrangian lattice Boltzmann method for the compressible flows
NASA Astrophysics Data System (ADS)
Yan, Guangwu; Dong, Yinfeng; Liu, Yanhong
2006-08-01
In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results.
Static contact angle in lattice Boltzmann models of immiscible fluids.
Latva-Kokko, M; Rothman, Daniel H
2005-10-01
We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes. PMID:16383561
Permeability of Partially Molten Rocks from Lattice-Boltzmann Modeling
NASA Astrophysics Data System (ADS)
Garapic, G.; Faul, U.
2013-12-01
Timescales of melt transport at mid-ocean ridges from mantle source to the surface depend on permeability of the partially molten mantle. The permeability is usually predicted indirectly from experimental observations based on porosities that are much higher than the porosities inferred for the partially molten mantle. Low porosities are for example predicted by geochemical models from the onset of melt migration. Since melting starts at the grain scale, permeability of the partially molten mantle will depend on the grain-scale melt distribution. We reconstructed a 3-D view of melt geometry of two experimentally produced samples of partially molten olivine which demonstrates that melt exists in thin layers on two-grain boundaries (Garapić et al.,G3, 2013). The wetted two-grain boundaries have a width about 100 times smaller than the average grain size. Additionally, the pore space consists of a network of triple-junction tubules at all porosities, and large 'melt pools'. Due to the relative size of the wetted two-grain boundaries as well as the size of the triple-junction network compared to the grain size imagining and numerical analyses of partially molten samples require high resolution. Since no direct experimental permeability measurements are possible on partially molten aggregates, we investigate numerically the permeability as a function of porosity for this system. We simulate porous flow through an artificial pore volume using the lattice-Boltzmann method (LBM) and Palabos LB code. Flow simulations were done on a computer cluster on three or four 125 GB nodes with 16 processors per node. With the available memory and allowed run time the maximum size of our pore structure was 1100 voxels per edge. In its simplest form the pore structure consists of a network of cylinders within a matrix of cubic grains. To approximate the observed 3-D melt geometry we added randomly distributed sheets on cube faces ('wetted two-grain boundaries') as well as randomly
Lattice Boltzmann model for a steady radiative transfer equation.
Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping
2016-08-01
A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed. PMID:27627417
Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media
NASA Astrophysics Data System (ADS)
Karani, Hamid; Huber, Christian
2015-02-01
In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics
Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems
Uddin, Rizwan
2012-01-01
This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.
NASA Astrophysics Data System (ADS)
Yu, Huidan; Chen, Xi; Wang, Zhiqiang; Deep, Debanjan; Lima, Everton; Zhao, Ye; Teague, Shawn D.
2014-06-01
In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter P (x,y,z,t) defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, P =1), fluid cell (pure fluid occupation, P =0), and boundary cell (partial solid and partial fluid, 0
lattice Boltzmann equations are self-regularized through P and consist of three parts: (1) collision taking into account the momentum exchange between the willfully moving boundary and the flow; (2) streaming accompanying a volumetric bounce-back procedure in boundary cells; and (3) boundary-induced volumetric fluid migration moving the residual fluid particles into the flow domain when the boundary swipes over a boundary cell toward a solid cell. The MCVLBM strictly satisfies mass conservation and can handle irregular boundary orientation and motion with respect to the mesh. Validation studies are carried out in four cases. The first is to simulate fluid dynamics in syringes focusing on how MCVLBM captures the underlying physics of flow driven by a willfully moving piston. The second and third cases are two-dimensional (2D) peristaltic flow and three-dimensional (3D) pipe flow, respectively. In each case, we compare the MCVLBM simulation result with the analytical solution and achieve quantitatively good agreements. The fourth case is to simulate blood flow in human aortic arteries with a very complicated irregular boundary. We study steady flow in two dimensions and unsteady flow via the pulsation of the cardiac cycle in three dimensions. In the 2D case, both vector (velocity) and
Large-scale lattice-Boltzmann simulations over lambda networks
NASA Astrophysics Data System (ADS)
Saksena, R.; Coveney, P. V.; Pinning, R.; Booth, S.
Amphiphilic molecules are of immense industrial importance, mainly due to their tendency to align at interfaces in a solution of immiscible species, e.g., oil and water, thereby reducing surface tension. Depending on the concentration of amphiphiles in the solution, they may assemble into a variety of morphologies, such as lamellae, micelles, sponge and cubic bicontinuous structures exhibiting non-trivial rheological properties. The main objective of this work is to study the rheological properties of very large, defect-containing gyroidal systems (of up to 10243 lattice sites) using the lattice-Boltzmann method. Memory requirements for the simulation of such large lattices exceed that available to us on most supercomputers and so we use MPICH-G2/MPIg to investigate geographically distributed domain decomposition simulations across HPCx in the UK and TeraGrid in the US. Use of MPICH-G2/MPIg requires the port-forwarder to work with the grid middleware on HPCx. Data from the simulations is streamed to a high performance visualisation resource at UCL (London) for rendering and visualisation. Lighting the Blue Touchpaper for UK e-Science - Closing Conference of ESLEA Project March 26-28 2007 The George Hotel, Edinburgh, UK
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential
Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid
NASA Astrophysics Data System (ADS)
Papenkort, S.; Voigtmann, Th.
2015-07-01
We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation.
Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid.
Papenkort, S; Voigtmann, Th
2015-07-28
We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation. PMID:26233150
Gauss Quadratures - the Keystone of Lattice Boltzmann Models
NASA Astrophysics Data System (ADS)
Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor
2014-01-01
In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation
NASA Technical Reports Server (NTRS)
Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q.
2015-01-01
A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.
Lattice-Boltzmann hydrodynamics of anisotropic active matter.
de Graaf, Joost; Menke, Henri; Mathijssen, Arnold J T M; Fabritius, Marc; Holm, Christian; Shendruk, Tyler N
2016-04-01
A plethora of active matter models exist that describe the behavior of self-propelled particles (or swimmers), both with and without hydrodynamics. However, there are few studies that consider shape-anisotropic swimmers and include hydrodynamic interactions. Here, we introduce a simple method to simulate self-propelled colloids interacting hydrodynamically in a viscous medium using the lattice-Boltzmann technique. Our model is based on raspberry-type viscous coupling and a force/counter-force formalism, which ensures that the system is force free. We consider several anisotropic shapes and characterize their hydrodynamic multipolar flow field. We demonstrate that shape-anisotropy can lead to the presence of a strong quadrupole and octupole moments, in addition to the principle dipole moment. The ability to simulate and characterize these higher-order moments will prove crucial for understanding the behavior of model swimmers in confining geometries. PMID:27059561
Lattice-Boltzmann hydrodynamics of anisotropic active matter
NASA Astrophysics Data System (ADS)
de Graaf, Joost; Menke, Henri; Mathijssen, Arnold J. T. M.; Fabritius, Marc; Holm, Christian; Shendruk, Tyler N.
2016-04-01
A plethora of active matter models exist that describe the behavior of self-propelled particles (or swimmers), both with and without hydrodynamics. However, there are few studies that consider shape-anisotropic swimmers and include hydrodynamic interactions. Here, we introduce a simple method to simulate self-propelled colloids interacting hydrodynamically in a viscous medium using the lattice-Boltzmann technique. Our model is based on raspberry-type viscous coupling and a force/counter-force formalism, which ensures that the system is force free. We consider several anisotropic shapes and characterize their hydrodynamic multipolar flow field. We demonstrate that shape-anisotropy can lead to the presence of a strong quadrupole and octupole moments, in addition to the principle dipole moment. The ability to simulate and characterize these higher-order moments will prove crucial for understanding the behavior of model swimmers in confining geometries.
Finite-difference lattice-Boltzmann methods for binary fluids.
Xu, Aiguo
2005-06-01
We investigate two-fluid Bhatnagar-Gross-Krook (BGK) kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D, and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior. PMID:16089910
Full Eulerian lattice Boltzmann model for conjugate heat transfer
NASA Astrophysics Data System (ADS)
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.
Two relaxation time lattice Boltzmann model for rarefied gas flows
NASA Astrophysics Data System (ADS)
Esfahani, Javad Abolfazli; Norouzi, Ali
2014-01-01
In this paper, the lattice Boltzmann equation (LBE) with two relaxation times (TRT) is implemented in order to study gaseous flow through a long micro/nano-channel. A new relation is introduced for the reflection factor in the bounce-back/specular reflection (BSR) boundary condition based on the analytical solution of the Navier-Stokes equations. The focus of the present study is on comparing TRT with the other LBE models called multiple relaxation times (MRT) and single relaxation time (SRT) in simulation of rarefied gas flows. After a stability analysis for the TRT and SRT models, the numerical results are presented and validated by the analytical solution of the Navier-Stokes equations with slip boundary condition, direct simulation of Monte Carlo (DSMC) and information preservation (IP) method. The effect of various gases on flow behavior is also investigated by using the variable hard sphere (VHS) model through the symmetrical relaxation time.
Lattice Boltzmann method for mixtures at variable Schmidt number
NASA Astrophysics Data System (ADS)
Monteferrante, Michele; Melchionna, Simone; Marconi, Umberto Marini Bettolo
2014-07-01
When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.
Lattice Boltzmann method for mixtures at variable Schmidt number.
Monteferrante, Michele; Melchionna, Simone; Marconi, Umberto Marini Bettolo
2014-07-01
When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity. PMID:25005272
Modeling of urban traffic networks with lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Meng, Jian-ping; Qian, Yue-hong; Dai, Shi-qiang
2008-02-01
It is of great importance to uncover the characteristics of traffic networks. However, there have been few researches concerning kinetics models for urban traffic networks. In this work, a lattice Boltzmann model (LBM) for urban traffic networks is proposed by incorporating the ideas of the Biham-Middleton-Levine (BML) model into the LBM for road traffic. In the present model, situations at intersections with the red and green traffic signals are treated as a kind of boundary conditions varying with time. Thus, the urban traffic network could be described in the mesoscopic level. By performing numerical simulations under the periodic boundary conditions, the behavior of average velocity is investigated in detail. The numerical results agree quite well with those given by the Chowdhury-Schadschneider (ChSch) model (Chowdhury D. and Schadschneider A., Phys. Rev. E, 59 (1999) R1311). Furthermore, the statistical noise is reduced in this discrete kinetics model, thus, the present model has considerably high computational efficiency.
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. PMID:20590325
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation
NASA Technical Reports Server (NTRS)
Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q
2015-01-01
A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.
Lattice-Boltzmann Simulation of Coalescence-Driven Island Coarsening
Hakan Basagaoglu; Christopher T. Green; Paul Meakin; Benjamin J. McCoy
2004-10-01
A two-dimensional lattice-Boltzmann model (LBM) with fluid-fluid interactions was used to simulate first-order phase separation in a thin fluid film. The intermediate asymptotic time dependence of the mean island size, island number concentration, and polydispersity were determined and compared with the predictions of the distribution-kinetics model. The comparison revealed that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations. However, the overall process is dominated by coalescence, which is independent of island mass. As the phase transition advances, the mean island size increases, the number of islands decrease, and the polydispersity approaches unity, which conforms to the predictions of the distribution-kinetics model. The effects of the domain size on the intermediate asymptotic island size distribution, scaling form of the island size distribution, and the crossover to the long-term asymptotic behavior were elucidated. (C) 2004 American Institute of Physics.
Full Eulerian lattice Boltzmann model for conjugate heat transfer.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results. PMID:26764851
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Influence of asperities on fluid and thermal flow in a fracture: A coupled lattice Boltzmann study
NASA Astrophysics Data System (ADS)
Neuville, A.; Flekkøy, E. G.; Toussaint, R.
2013-07-01
The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier-Stokes and advection-diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three-dimensional (3-D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two-dimensional (integrated over the thickness) advection-diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic lattices. Beyond some critical slope for the boundaries, the velocity profile is observed to be far from a quadratic profile in the vicinity of the sharp asperity: the fluid within the triangular asperity is quasi-static. We find that taking account of both the 3-D effects and the cooling of the rock, are important for the thermal exchange. Neglecting these effects with lubrication approximations results in overestimating the heat exchange efficiency. The evolution of the temperature over time, toward steady state, also shows complex behavior: some sites alternately reheat and cool down several times, making it difficult to forecast the extracted heat.
A Three-Dimensional Multi-Mesh Lattice Boltzmann Model for Multiphysics Simulations
NASA Astrophysics Data System (ADS)
Hashemi, Amirreza; Eshraghi, Mohsen; Felicelli, Sergio
2015-11-01
The lattice Boltzmann method (LBM) is known as an attractive computational method for modeling fluid flow and, more recently, transport phenomena. As any numerical method, the computational cost of LBM simulations depends on the density of the computational grids. The cost of simulations can become enormous when multiple equations are solved in three dimensions. In this work, the development of a multi-block multi-grid LBM model is discussed for three-dimensional (3D) multiphysics simulations. In a system of multiple coupled equations with different length scales, a multi-block mesh with different grids for each model would enhance the computational efficiency and stability of the model. Embedded-type grids facilitate the transfer of information between lattices while allowing larger time steps. In addition, a non-uniform mesh is considered within each mode that allows mesh refinement within each physical model when required. The multi-mesh method was developed to solve for transport phenomena including fluid flow, mass and heat transfer. The huge memory demands of LBM simulations in 3D was significantly reduced using this scheme. Moreover, by reducing the number of lattice points, cost communication in parallel processing was largely decreased.
Towards Full Aircraft Airframe Noise Prediction: Lattice Boltzmann Simulations
NASA Technical Reports Server (NTRS)
Khorrami, Mehdi R.; Fares, Ehab; Casalino, Damiano
2014-01-01
Computational results for an 18%-scale, semi-span Gulfstream aircraft model are presented. Exa Corporation's lattice Boltzmann PowerFLOW(trademark) solver was used to perform time-dependent simulations of the flow field associated with this high-fidelity aircraft model. The simulations were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg (landing configuration). We focused on accurately predicting the prominent noise sources at the flap tips and main landing gear for the two baseline configurations, namely, landing flap setting without and with gear deployed. Capitalizing on the inherently transient nature of the lattice Boltzmann formulation, the complex time-dependent flow features associated with the flap were resolved very accurately and efficiently. To properly simulate the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips. Extensive comparison of the computed time-averaged and unsteady surface pressures with wind tunnel measurements showed excellent agreement for the global aerodynamic characteristics and the local flow field at the flap inboard and outboard tips and the main landing gear. In particular, the computed fluctuating surface pressure field for the flap agreed well with the measurements in both amplitude and frequency content, indicating that the prominent airframe noise sources at the tips were captured successfully. Gear-flap interaction effects were remarkably well predicted and were shown to affect only the inboard flap tip, altering the steady and unsteady pressure fields in that region. The simulated farfield noise spectra for both baseline configurations, obtained using a Ffowcs-Williams and Hawkings acoustic analogy approach, were shown to be in close agreement with measured values.
Study of three-dimensional electro-osmotic flow with curved boundary via lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Chen, Q.; Zhang, X. B.; Li, Q.; Jiang, X. S.; Zhou, H. P.
2016-01-01
A three-dimensional (3D) lattice Boltzmann model and boundary method is developed to simulate electro-osmotic flow (EOF) with a charged spherical particle immersed in an electrolyte solution. The general governing equations for electro-osmotic transport are Navier-Stokes equations for fluid flow and the Poisson-Boltzmann equation for electric potential distribution around the particle. Two sets of D3Q19 lattice structure with curved boundary conditions are implemented. The simulation results are compared with analytical predictions and are found to be in excellent agreement. The potential distribution appears circularly symmetric and the flow velocity decreases with the cross-sectional area for flow passage increasing due to the mass conservation. The effects of the ionic concentration, the sphere radius, electric potential and external electric field on the velocity profiles are investigated. The flow velocity increases with both the electric potential and the external electric field. However, the variation in flow velocity with the ionic concentration and the sphere radius is complex due to the change in electrical double layer (EDL) thickness.
One-dimensional transient radiative transfer by lattice Boltzmann method.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2013-10-21
The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed. PMID:24150298
Volumetric lattice Boltzmann simulation for blood flow in aorta arteries
NASA Astrophysics Data System (ADS)
Deep, Debanjan; Yu, Huidan (Whitney); Teague, Shawn
2012-11-01
Complicated moving boundaries pose a major challenge in computational fluid dynamics for complex flows, especially in the biomechanics of both blood flow in the cardiovascular system and air flow in the respiratory system where the compliant nature of the vessels can have significant effects on the flow rate and wall shear stress. We develop a computation approach to treat arbitrarily moving boundaries using a volumetric representation of lattice Boltzmann method, which distributes fluid particles inside lattice cells. A volumetric bounce-back procedure is applied in the streaming step while momentum exchange between the fluid and moving solid boundary are accounted for in the collision sub-step. Additional boundary-induced migration is introduced to conserve fluid mass as the boundary moves across fluid cells. The volumetric LBM (VLBM) is used to simulate blood flow in both normal and dilated aorta arteries. We first compare flow structure and pressure distribution in steady state with results from Navier-Stokes based solver and good agreements are achieved. Then we focus on wall stress within the aorta for different heart pumping condition and present quantitative measurement of wall shear and normal stress.
Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates
NASA Astrophysics Data System (ADS)
Budinski, Ljubomir; Fabian, Julius; Stipic, Matija
2015-07-01
In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of modeling flow in domains of complex geometry with the opportunity of local refining/coarsening of the computational mesh corresponding to the complexity of the flow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of flow implemented in the equilibrium function, finding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely verified by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater flow in complex flow domains.
Evaluation of the Lattice-Boltzmann Equation Solver PowerFLOW for Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Lockard, David P.; Luo, Li-Shi; Singer, Bart A.; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
A careful comparison of the performance of a commercially available Lattice-Boltzmann Equation solver (Power-FLOW) was made with a conventional, block-structured computational fluid-dynamics code (CFL3D) for the flow over a two-dimensional NACA-0012 airfoil. The results suggest that the version of PowerFLOW used in the investigation produced solutions with large errors in the computed flow field; these errors are attributed to inadequate resolution of the boundary layer for reasons related to grid resolution and primitive turbulence modeling. The requirement of square grid cells in the PowerFLOW calculations limited the number of points that could be used to span the boundary layer on the wing and still keep the computation size small enough to fit on the available computers. Although not discussed in detail, disappointing results were also obtained with PowerFLOW for a cavity flow and for the flow around a generic helicopter configuration.
Lattice Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook hydrodynamics of quantum gases
NASA Astrophysics Data System (ADS)
Yang, Jaw-Yen; Hung, Li-Hsin
2009-05-01
We present a semiclassical lattice Boltzmann method based on quantum kinetic theory. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook equations onto the tensor Hermite polynomials following Grad’s moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. Gases of particles of arbitrary statistics can be considered. Simulation of one-dimensional compressible gas flow and two-dimensional hydrodynamic flows are shown. The results indicate distinct characteristics of the effects of quantum statistics.
Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Velasco, Ali Mauricio; Muñoz, José Daniel
2015-10-01
Rayleigh-Taylor and Kelvin-Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil-water one. The model, proposed by He, Chen and Zhang (1999) [1] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [2]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation γ ∝√{ A} between the growing rate γ of the Rayleigh-Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.
Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry
NASA Technical Reports Server (NTRS)
Mei, Renwei; Yu, Dazhi; Shyy, Wei; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.
Lattice Boltzmann modeling of directional wetting: comparing simulations to experiments.
Jansen, H Patrick; Sotthewes, Kai; van Swigchem, Jeroen; Zandvliet, Harold J W; Kooij, E Stefan
2013-07-01
Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting. PMID:23944550
Lattice Boltzmann modeling of three-phase incompressible flows.
Liang, H; Shi, B C; Chai, Z H
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems. PMID:26871191
Consistent lattice Boltzmann methods for incompressible axisymmetric flows.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407
Thermal multicomponent lattice Boltzmann model for catalytic reactive flows.
Kang, Jinfen; Prasianakis, Nikolaos I; Mantzaras, John
2014-06-01
Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model. PMID:25019915
Dynamic permeability of porous media by the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Pazdniakou, A.; Adler, P. M.
2013-12-01
The lattice Boltzmann method (LBM) is applied to calculate the dynamic permeability K(ω) of porous media; an oscillating macroscopic pressure gradient is imposed in order to generate oscillating flows. The LBM simulation yields the time dependent seepage velocity of amplitude A and phase shift B which are used to calculate K(ω). The procedure is validated for plane Poiseuille flows where excellent agreement with the analytical solution is obtained. The limitations of the method are discussed. When the ratio between the kinematic viscosity and the characteristic size of the pores is high, the corresponding Knudsen number Kn is high and the numerical values of K(ω) are incorrect with a positive imaginary part; it is only when Kn is small enough that correct values are obtained. The influence of the time discretization of the oscillating body force is studied; simulation results are influenced by an insufficient discretization, i.e., it is necessary to avoid using too high frequencies. The influence of absolute errors in the seepage velocity amplitude δA and the phase shift δB on K(ω) shows that for high ω even small errors in B can cause drastic errors in ReK(ω). The dynamic permeability of reconstructed and real (sandstone) porous media is calculated for a large range of frequencies and the universal scaling behavior is verified. Very good correspondences with the theoretical predictions are observed.
Lattice Boltzmann modeling of three-phase incompressible flows
NASA Astrophysics Data System (ADS)
Liang, H.; Shi, B. C.; Chai, Z. H.
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
Multiblock approach for the passive scalar thermal lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2014-04-01
A multiblock approach for the passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time collision scheme is proposed based on the Chapman-Enskog analysis. The interaction between blocks is executed in the moment space directly and an external force term is considered. Theoretical analysis shows that all the nonequilibrium parts of the nonconserved moments should be rescaled, while the nonequilibrium parts of the conserved moments can be calculated directly. Moreover, a local scheme based on the pseudoparticles for computing heat flux is proposed with no need to calculate temperature gradient based on the finite-difference scheme. In order to validate the multiblock approach and local scheme for computing heat flux, thermal Couette flow with wall injection is simulated and good results are obtained, which show that the adoption of the multiblock approach does not deteriorate the convergence rate of TLBM and the local scheme for computing heat flux has second-order convergence rate. Further application of the present approach is the simulation of natural convection in a square cavity with the Rayleigh number up to 109.
Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.
Li, Q; Luo, K H; Li, X J
2012-07-01
The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model. PMID:23005565
Force evaluation in the lattice Boltzmann method involving curved geometry
NASA Astrophysics Data System (ADS)
Mei, Renwei; Yu, Dazhi; Shyy, Wei; Luo, Li-Shi
2002-04-01
The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei et al., J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.
Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles
NASA Astrophysics Data System (ADS)
Zhang, Pei; Galindo-Torres, S. A.; Tang, Hongwu; Jin, Guangqiu; Scheuermann, A.; Li, Ling
2016-06-01
We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100 . The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.
Lattice Boltzmann Modeling of Micro-fluidic Devices
Clague, D S
2002-01-28
The results to date do indeed show that the lattice Boltzmann method accurately solves relevant, non-trivial flow problems. The parallelization of both the fluid and the mobile species in flow has enhanced this capability such that it is useful for solving relevant problems in a timely fashion. The initial studies of stationary or capture species revealed evidence of hydrodynamic screening between upstream and downstream particles. Numerical studies reveal that the critical length for which the test particle is hydrodynamically decoupled from upstream and downstream particles is on the order of 30 sphere radii. For mobile species, the LB capability was shown to be naturally suited for predicting the hydrodynamic lift phenomenon (inertial lift). A conversion factor was developed based on scaling arguments to include relevant forces generated by external fields. Using this conversion, an analytic solution for the Dielectrophoretic force was included into the LB capability which enabled the study of Dielectrophoretic particle capture. The Non-Newtonian enhancements have expanded the applicability of the LB capability to more physical systems. Specifically, with the bead-n-spring representation of macromolecules researchers will be able to study chain dynamics in micro-, physiological and Bio-MEMS environments. Furthermore, the ability to capture the shear thinning behavior, without any increase in computational time, positions this capability to be applied to a whole host of new problems involving biofluids.
Thermal multicomponent lattice Boltzmann model for catalytic reactive flows
NASA Astrophysics Data System (ADS)
Kang, Jinfen; Prasianakis, Nikolaos I.; Mantzaras, John
2014-06-01
Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013), 10.1103/PhysRevE.87.053304] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008), 10.1103/PhysRevE.78.046711] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.
Lattice Boltzmann simulations of drops colliding with solid surfaces
NASA Astrophysics Data System (ADS)
Jia, X.; McLaughlin, J. B.; Kontomaris, K.
2009-04-01
Video images of drops colliding with solid surfaces shown by Rioboo et al. (2002) reveal that, for large drop velocities, the drops flatten and form a ring structure before receding and, in some cases, rebounding from the surface. They described the sequence of events in terms of four distinct regimes. During the initial kinematic phase, the dimensionless wetting radius of the drop follows a universal form if the drop Weber and Reynolds numbers are sufficiently large. In the second phase, the drop becomes highly flattened and the values of the Weber and Reynolds numbers influence the time evolution of the dimensionless wetting radius and its maximum value. This is followed by a third phase in which the wetting radius begins to decrease with time and the wettability of the surface influences the dynamics. This paper presents simulation results for the early stages of drop impact and spreading on a partially wetting solid surface. The simulations were performed with a modified version of the lattice Boltzmann method (LBM) developed by Inamuro et al. (2004) for a liquid-gas density ratio of 1000. The Inamuro et al. version of the LBM was modified by incorporating rigid, no-slip boundary conditions and incorporating a boundary condition on the normal derivative of the order parameter to impose the desired equilibrium contact angle.
Massively parallel simulations of multiphase flows using Lattice Boltzmann methods
NASA Astrophysics Data System (ADS)
Ahrenholz, Benjamin
2010-03-01
In the last two decades the lattice Boltzmann method (LBM) has matured as an alternative and efficient numerical scheme for the simulation of fluid flows and transport problems. Unlike conventional numerical schemes based on discretizations of macroscopic continuum equations, the LBM is based on microscopic models and mesoscopic kinetic equations. The fundamental idea of the LBM is to construct simplified kinetic models that incorporate the essential physics of microscopic or mesoscopic processes so that the macroscopic averaged properties obey the desired macroscopic equations. Especially applications involving interfacial dynamics, complex and/or changing boundaries and complicated constitutive relationships which can be derived from a microscopic picture are suitable for the LBM. In this talk a modified and optimized version of a Gunstensen color model is presented to describe the dynamics of the fluid/fluid interface where the flow field is based on a multi-relaxation-time model. Based on that modeling approach validation studies of contact line motion are shown. Due to the fact that the LB method generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallelization. Hence, it is possible to perform efficient simulations in complex geometries at a large scale by massively parallel computations. Here, the results of drainage and imbibition (Degree of Freedom > 2E11) in natural porous media gained from microtomography methods are presented. Those fully resolved pore scale simulations are essential for a better understanding of the physical processes in porous media and therefore important for the determination of constitutive relationships.
Lattice Boltzmann method for one-dimensional vector radiative transfer.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2016-02-01
A one-dimensional vector radiative transfer (VRT) model based on lattice Boltzmann method (LBM) that considers polarization using four Stokes parameters is developed. The angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by LBM. LBM has such attractive properties as simple calculation procedure, straightforward and efficient handing of boundary conditions, and capability of stable and accurate simulation. To validate the performance of LBM for vector radiative transfer, four various test problems are examined. The first case investigates the non-scattering thermal-emitting atmosphere with no external collimated solar. For the other three cases, the external collimated solar and three different scattering types are considered. Particularly, the LBM is extended to solve VRT in the atmospheric aerosol system where the scattering function contains singularities and the hemisphere space distributions for the Stokes vector are presented and discussed. The accuracy and computational efficiency of this algorithm are discussed. Numerical results show that the LBM is accurate, flexible and effective to solve one-dimensional polarized radiative transfer problems. PMID:26906779
Large Eddy Simulations using Lattice Boltzmann algorithms. Final report
Serling, J.D.
1993-09-28
This report contains the results of a study performed to implement eddy-viscosity models for Large-Eddy-Simulations (LES) into Lattice Boltzmann (LB) algorithms for simulating fluid flows. This implementation requires modification of the LB method of simulating the incompressible Navier-Stokes equations to allow simulation of the filtered Navier-Stokes equations with some subgrid model for the Reynolds stress term. We demonstrate that the LB method can indeed be used for LES by simply locally adjusting the value of the BGK relaxation time to obtain the desired eddy-viscosity. Thus, many forms of eddy-viscosity models including the standard Smagorinsky model or the Dynamic model may be implemented using LB algorithms. Since underresolved LB simulations often lead to instability, the LES model actually serves to stabilize the method. An alternative method of ensuring stability is presented which requires that entropy increase during the collision step of the LB method. Thus, an alternative collision operator is locally applied if the entropy becomes too low. This stable LB method then acts as an LES scheme that effectively introduces its own eddy viscosity to damp short wavelength oscillations.
Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes
NASA Astrophysics Data System (ADS)
Ginzburg, Irina
2013-01-01
This paper develops a symmetrized framework for the analysis of the anisotropic advection-diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
NASA Astrophysics Data System (ADS)
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
Lattice Boltzmann simulation for forced two-dimensional turbulence.
Xia, YuXian; Qian, YueHong
2014-08-01
The direct numerical simulations of forced two-dimensional turbulent flow are presented by using the lattice Boltzmann method. The development of an energy-enstrophy double cascade is investigated in the two cases of external force of two-dimensional turbulence, Gaussian force and Kolmogorov force. It is found that the friction force is a necessary condition of the occurrence of a double cascade. The energy spectrum k(-3) in the enstrophy inertial range is in accord with the classical Kraichnan theory for both external forces. The energy spectrum of the Gaussian force case in an inverse cascade is k(-2); however, the Kolmogorov force drives the k(-5/3) energy in a backscatter cascade. The result agrees with Scott's standpoint, which describes nonrobustness of the two-dimensional turbulent inverse cascade. Also, intermittency is found for the enstrophy cascade in two cases of the external force form. Intermittency refers to the nonuniform distribution of saddle points in the two-dimensional turbulent flow. PMID:25215817
Lattice Boltzmann simulation for forced two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Xia, YuXian; Qian, YueHong
2014-08-01
The direct numerical simulations of forced two-dimensional turbulent flow are presented by using the lattice Boltzmann method. The development of an energy-enstrophy double cascade is investigated in the two cases of external force of two-dimensional turbulence, Gaussian force and Kolmogorov force. It is found that the friction force is a necessary condition of the occurrence of a double cascade. The energy spectrum k-3 in the enstrophy inertial range is in accord with the classical Kraichnan theory for both external forces. The energy spectrum of the Gaussian force case in an inverse cascade is k-2; however, the Kolmogorov force drives the k-5/3 energy in a backscatter cascade. The result agrees with Scott's standpoint, which describes nonrobustness of the two-dimensional turbulent inverse cascade. Also, intermittency is found for the enstrophy cascade in two cases of the external force form. Intermittency refers to the nonuniform distribution of saddle points in the two-dimensional turbulent flow.
Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms
Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine
2008-02-01
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 14x improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
Treatment of moving boundaries in lattice-Boltzmann simulations.
NASA Astrophysics Data System (ADS)
Indireshkumar, K.; Pal, A.; Brasseur, J. G.
2000-11-01
We consider the treatment of moving boundaries with the lattice-Boltzmann (LB) technique, where the treatment of the boundary often does not precisely conserve mass and spurious fluctuations in density/pressure result from boundary motion through fixed grids. First, we applied the extrapolation method proposed by Chen et. al.(S. Y. Chen, D. Martinez, and R Mei, Phys. Fluids) 8, 2527 (1996) to incompressible flow induced by the movement of a piston in a 2D ``cylinder'' with mass flow out of or into the cylinder. In these simulations, the velocity of the boundary nodes is set equal to the (known) velocity of the boundary (piston) in the equilibrium distribution function (Method I). In a second set of simulations, the boundary node velocities are obtained by interpolating between interior nodes and the boundary, thus including the effect of boundary position more precisely (Method II). Comparison of LB predictions with simulations using FIDAP show pressure agreement to witnin 2 %. The total mass is conserved to within 0.1% with Method I and improves to within 0.02 % using method II. Spurious fluctuations in density/pressure due to boundary movement is about 0.9% with Method I, which improves significantly to about 0.3% with Method II. The application of these simple techniques to more complex geometries and wall (and fluid) motions in a stomach during gastric emptying will be presented.
Dynamic permeability of porous media by the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Adler, P.; Pazdniakou, A.
2012-04-01
The main objective of our work is to determine the dynamic permeability of three dimensional porous media by means of the Lattice Boltzmann method (LBM). The Navier-Stokes equation can be numerically solved by LBM which is widely used to address various fluid dynamics problems. Space is discretized by a three-dimensional cubic lattice and time is discretized as well. The generally accepted notation for lattice Boltzmann models is DdQq where D stands for space dimension and Q for the number of discrete velocities. The present model is denoted by D3Q19. Moreover, the Two Relaxation Times variant of the Multi Relaxation Times model is implemented. Bounce back boundary conditions are used on the solid-fluid interfaces. The porous medium is spatially periodic. Reconstructed media were used; they are obtained by imposing a porosity and a correlation function characterized by a correlation length. Real samples can be obtained by MicroCT. In contrast with other previous contributions, the dynamic permeability K(omega) which is a complex number, is derived by imposing an oscillating body force of pulsation omega on the unit cell and by deriving the amplitude and the phase shift of the resulting time dependent seepage velocity. The influence of two limiting parameters, namely the Knudsen number Kn and the discretization for high frequencies, on K(omega) is carefully studied for the first time. Kn is proportional to nu/(cs H) where nu is the kinematic viscosity, cs the speed of sound in the fluid and H a characteristic length scale of the porous medium. Several porous media such as the classical plane Poiseuille flow and the reconstructed media are used to show that it is only for small enough values of Kn that reliable results are obtained. Otherwise, the data depend on Kn and may even be totally unphysical. However, it should be noticed that the limiting value of Kn could not be derived in general since it depends very much on the structure of the medium. Problems occur at
Dynamic permeability of porous media by the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Pazdniakou, A.; Adler, P. M.
2011-12-01
The main objective of our work is to determine the dynamic permeability of three dimensional porous media by means of the Lattice Boltzmann method (LBM). The Navier-Stokes equation can be numerically solved by LBM which is widely used to address various fluid dynamics problems. Space is discretized by a three-dimensional cubic lattice and time is discretized as well. The generally accepted notation for lattice Boltzmann models is DdQq where D stands for space dimension and Q for the number of discrete velocities. The present model is denoted by D3Q19. Moreover, the Two Relaxation Times variant of the Multi Relaxation Times model is implemented. Bounce back boundary conditions are used on the solid-fluid interfaces. The porous medium is spatially periodic. Reconstructed media were used; they are obtained by imposing a porosity and a correlation function characterized by a correlation length. Real samples can be obtained by MicroCT. In contrast with other previous contributions, the dynamic permeability K(omega) which is a complex number, is derived by imposing an oscillating body force of pulsation omega on the unit cell and by deriving the amplitude and the phase shift of the resulting time dependent seepage velocity. The influence of two limiting parameters, namely the Knudsen number Kn and the discretization for high frequencies, on K(omega) is carefully studied for the first time. Kn is proportional to nu/(c_s H) where nu is the kinematic viscosity, c_s the speed of sound in the fluid and H a characteristic length scale of the porous medium. Several porous media such as the classical plane Poiseuille flow and the reconstructed media are used to show that it is only for small enough values of Kn that reliable results are obtained. Otherwise, the data depend on Kn and may even be totally unphysical. However, it should be noticed that the limiting value of Kn could not be derived in general since it depends very much on the structure of the medium. Problems occur
NASA Astrophysics Data System (ADS)
Zhang, Jianying; Yan, Guangwu
2016-04-01
A lattice Boltzmann model for solving the (2+1) dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a two-dimensional space, and the evolution of the model is about a spatial axis rather than time. The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Numerical results reproduce the phenomena of the fusion of necklace-ring pattern and the effect of non-linearity on the soliton in the CQCGLE.
NASA Astrophysics Data System (ADS)
Zhang, Jianying; Yan, Guangwu
2015-12-01
A spatiotemporal lattice Boltzmann model for solving the three-dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a three-dimensional spatiotemporal space, and the evolution of the model is about a spatial axis rather than time. The algorithm possesses advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Examples show that the model reproduces the phenomena in the CQCGLE accurately.
Hybrid lattice-Boltzmann and finite-difference simulation of electroosmotic flow in a microchannel
NASA Astrophysics Data System (ADS)
Masilamani, Kannan; Ganguly, Suvankar; Feichtinger, Christian; Rüde, Ulrich
2011-04-01
A three-dimensional (3D) transient mathematical model is developed to simulate electroosmotic flows (EOFs) in a homogeneous, square cross-section microchannel, with and without considering the effects of axial pressure gradients. The general governing equations for electroosmotic transport are incompressible Navier-Stokes equations for fluid flow and the nonlinear Poisson-Boltzmann (PB) equation for electric potential distribution within the channel. In the present numerical approach, the hydrodynamic equations are solved using a lattice-Boltzmann (LB) algorithm and the PB equation is solved using a finite-difference (FD) method. The hybrid LB-FD numerical scheme is implemented on an iterative framework solving the system of coupled time-dependent partial differential equations subjected to the pertinent boundary conditions. Transient behavior of the EOF and effects due to the variations of different physicochemical parameters on the electroosmotic velocity profile are investigated. Transport characteristics for the case of combined electroosmotic- and pressure-driven microflows are also examined with the present model. For the sake of comparison, the cases of both favorable and adverse pressure gradients are considered. EOF behaviors of the non-Newtonian fluid are studied through implementation of the power-law model in the 3D LB algorithm devised for the fluid flow analysis. Numerical simulations reveal that the rheological characteristic of the fluid changes the EOF pattern to a considerable extent and can have significant consequences in the design of electroosmotically actuated bio-microfluidic systems. To improve the performance of the numerical solver, the proposed algorithm is implemented for parallel computing architectures and the overall parallel performance is found to improve with the number of processors.
Multigrid lattice Boltzmann method for accelerated solution of elliptic equations
NASA Astrophysics Data System (ADS)
Patil, Dhiraj V.; Premnath, Kannan N.; Banerjee, Sanjoy
2014-05-01
A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stone's strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V- or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.
Lattice Boltzmann description of magnetization in porous media
NASA Astrophysics Data System (ADS)
Guyer, R. A.; McCall, K. R.
2000-08-01
The magnetic moments of fluid particles filling the pore space of a porous material (1) reside in a complex space, (2) are carried by the particles in diffusive exploration of the pore space, and (3) relax when the particles approach relaxation sites on the walls of the pore space. Further, when the magnetic moments are the object of a nuclear magnetic resonance experiment, they are manipulated by rf magnetic fields, internal magnetic field gradients, and applied magnetic field gradient pulses. In this paper, a lattice Boltzmann computational procedure is described that accounts for all of the vagaries in the experience of a magnetic moment in a porous material. The time evolution of the longitudinal and transverse magnetization, in a variety of experimental situations, can be simulated with this computational procedure. The z component of the magnetization, the longitudinal magnetization, is described by a set of coarse grained distribution functions for a scalar fluid. The time evolution of these distribution functions involves a scattering process (to account for diffusion) and a probability of transmission out of the pore space (to account for surface relaxation). A numerical example, involving a pore adjacent to a microporous region, is examined in detail. The transverse magnetization is a vector. Its x and y magnetization components are carried by separate scalar fluids. There is a set of coarse grained distribution functions for each fluid. Radio frequency magnetic fields, internal magnetic field gradients, applied magnetic field gradient pulses, etc., represent conversion processes in which the two fluids transform into one another. Two examples, one involving a periodic field gradient and a Hahn echo, and the other involving an isolated pore and a PFG sequence, are examined in detail.
Force method in a pseudo-potential lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Hu, Anjie; Li, Longjian; Uddin, Rizwan
2015-08-01
Single component pseudo-potential lattice Boltzmann models have been widely studied due to their simplicity and stability in multiphase simulations. While numerous models have been proposed, comparative analysis and advantages and disadvantages of different force schemes are often lacking. A pseudo-potential model to simulate large density ratios proposed by Kupershtokh et al. [1] is analyzed in detail in this work. Several common used force schemes are utilized and results compared. Based on the numerical results, the relatively most accurate force scheme proposed by Guo et al. [2] is selected and applied to improve the accuracy of Kupershtokh et al.'s model. Results obtained using the modified Kupershtokh et al.'s model [1] for different value of τ are compared with those obtained using Li et al.'s model [3]. Effect of relaxation time τ on the accuracy of the results is reported. Moreover, it is noted that the error in the density ratio predicted by the model is directly correlated with the magnitude of the spurious velocities on (curved) interfaces. Simulation results show that, the accuracy of Kupershtokh et al.'s model can be improved with Guo et al.'s force scheme [2]. However, the errors and τ's effects are still noticeable when density ratios are large. To improve the accuracy of the pseudo-potential model and to reduce the effects of τ, two possible methods were discussed in the present work. Both, a rescaling of the equation of state and multi-relaxation time, are applied and are shown to improve the prediction of the density ratios.
Polar-coordinate lattice Boltzmann modeling of compressible flows
NASA Astrophysics Data System (ADS)
Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Succi, Sauro
2014-01-01
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.
Peristaltic particle transport using the Lattice Boltzmann method
Connington, Kevin William; Kang, Qinjun; Viswanathan, Hari S; Abdel-fattah, Amr; Chen, Shiyi
2009-01-01
Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.
An immersed boundary-lattice Boltzmann method for single- and multi-component fluid flows
NASA Astrophysics Data System (ADS)
Li, Zhe; Favier, Julien; D'Ortona, Umberto; Poncet, Sébastien
2016-01-01
The paper presents a numerical method to simulate single- and multi-component fluid flows around moving/deformable solid boundaries, based on the coupling of Immersed Boundary (IB) and Lattice Boltzmann (LB) methods. The fluid domain is simulated with LB method using the single relaxation time BGK model, in which an interparticle potential model is applied for multi-component fluid flows. The IB-related force is directly calculated with the interpolated definition of the fluid macroscopic velocity on the Lagrangian points that define the immersed solid boundary. The present IB-LB method can better ensure the no-slip solid boundary condition, thanks to an improved spreading operator. The proposed method is validated through several 2D/3D single- and multi-component fluid test cases with a particular emphasis on wetting conditions on solid wall. Finally, a 3D two-fluid application case is given to show the feasibility of modeling the fluid transport via a cluster of beating cilia.
Application of the lattice Boltzmann/lattice gas technique to multi-fluid flow in porous media
Soll, W.E.; Chen, S.Y.; Eggert, K.G.; Grunau, D.W.; Janecky, D.R.
1994-03-01
The lattice Boltzmann approach to modeling fluid flow provides an efficient and reliable method for solving the Navier-Stokes equations and studying multi-fluid flow problems. In this paper, we report state of the art capabilities of our lattice Boltzmann simulator for single- and two-fluid flows in two- and three-dimensional problems. We review the development of the code and present some of the latest results. Some of the flexibility available in the model includes arbitrary pore space descriptions, wettability effects, surface tension relations, and chemical reactivity. Simulations of two-fluid flow through a digitized micromodel geometry, and through a high resolution, digitized sample of Berea sandstone are presented. Relative permeability as a function of wettability and capillary number is discussed. Integration of the lattice Boltzmann approach into larger scale models to build a more powerful tool for analyzing constitutive behavior is considered.
NASA Astrophysics Data System (ADS)
Abdelaziz, Ramadan; Sussumu Komori, Fabio
2015-04-01
Recently, Lattice Boltzmann Modelling (LBM) techniques attract many scientists in various fields of research. This work shows the capability for LBM to simulate the fluid flow and solute transport in porous and fracture media, additionally, how to study behavior of nanofluids submitted to a temperature gradient, which it is an important process in natural aquatic environments, water treatment, and other water related technologies. LBSim is used in this work as Lattice Boltzmann Model simulator software. In this article, a series of cases using the lattice Boltzmann method are presented, showing the capability of the method in simulating phenomena with fluid flow and heat transfer in porous media. Results show that the lattice Boltzmann method delivers reliable and helpful simulations for the analyses of processes in water related technologies. Thus, LBSim is a recommended tool for simulating fluid flow at laminar and turbulent condition, and heat and mass transport under complex geometry and boundary condition. parameter values. Keywords: Lattice Boltzmann Model, LBSim, Fractures Media, Porous Media, nanofluids
A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows
NASA Astrophysics Data System (ADS)
Li, Kai; Zhong, Cheng-Wen
2015-05-01
This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiple-relaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time (SRT) lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version. Project supported by the Innovation Fund for Aerospace Science and Technology of China (Grant No. 2009200066) and the Aeronautical Science Fund of China (Grant No. 20111453012).
NASA Technical Reports Server (NTRS)
Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)
2005-01-01
Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.
NASA Astrophysics Data System (ADS)
Biciuşcă, Tonino; Horga, Adrian; Sofonea, Victor
2015-10-01
We use a two-dimensional Lattice Boltzmann model to investigate the liquid-vapour phase separation in an isothermal van der Waals fluid. The model is based on the expansion of the distribution function up to the third order in terms of Hermite polynomials. In two dimensions, this model is an off-lattice one and has 16 velocities. The Corner Transport Upwind Scheme is used to evolve the corresponding distribution functions on a square lattice. The resulting code allows one to follow the liquid-vapour phase separation on lattices up to 4096 × 4096 nodes using a Tesla M2090 Graphics Processing Unit.
Fully-Lagrangian and Lattice-Boltzmann Methods for Solving Systems of Conservation Equations
NASA Astrophysics Data System (ADS)
Ancona, M. G.
1994-11-01
A class of "fully-Lagrangian" methods for solving systems of conservation equations is defined. The key step in formulating these methods is the definition of a new set of field variables for which Lagrangian discretization is trivial. Recently popular lattice-Boltzmann simulation schemes for solving such systems are shown to be a useful sub-class of these fully-Lagrangian methods in which (a) the conservation laws are satisfied at each grid point, (b) the Lagrangian variables are expanded perturbatively, and (c) discretization error is used to represent physics. Such schemes are typically derived using methods of kinetic theory. Our numerical analysis approach shows that the conventional physical derivation, while certainly valid and fruitful, is not essential, that it often confuses physics and numerics and that it can be unnecessarily constraining. For example, we show that lattice-Boltzmann-like methods can be non-perturbative and can be made higher-order, implicit and/or with non-uniform grids. Furthermore, our approach provides new perspective on the relationship between lattice-Boltzmann methods and finite-difference techniques. Among other things, we show that the lattice-Boltzmann schemes are only conditionally consistent and in some cases are identical to the well-known Dufort-Frankel method. Through this connection, the lattice-Boltzmann method provides a rational basis for understanding Dufort-Frankel and gives a pathway for its generalization. At the same time, that Dufort Frankel is no longer much used suggests that the lattice-Boltzmann approach might also share this fate.
Chiavazzo, Eliodoro; Karlin, Iliya V.; Gorban, Alexander N.; Boulouchos, Konstantinos
2010-10-15
A new framework of simulation of reactive flows is proposed based on a coupling between accurate reduced reaction mechanism and the lattice Boltzmann representation of the flow phenomena. The model reduction is developed in the setting of slow invariant manifold construction, and the simplest lattice Boltzmann equation is used in order to work out the procedure of coupling of the reduced model with the flow solver. Practical details of constructing slow invariant manifolds of a reaction system under various thermodynamic conditions are reported. The proposed method is validated with the two-dimensional simulation of a premixed counterflow flame in the hydrogen-air mixture. (author)
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids
NASA Astrophysics Data System (ADS)
Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping
2016-02-01
In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.
Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping
2016-02-01
In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work. PMID:26986441
Lattice Boltzmann simulation of a fluid flow around a triangular unit of three isothermal cylinders
NASA Astrophysics Data System (ADS)
Alinejad, J.
2016-01-01
The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the Bhatnagar-Gross-Krook model are used to simulate two-dimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.
Lattice Boltzmann Hydrodynamic and Transport Modeling of Everglades Mangrove Estuaries
NASA Astrophysics Data System (ADS)
Sukop, M. C.; Engel, V.
2010-12-01
Lattice Boltzmann methods are being developed and applied to simulate groundwater and surface water flows, and heat, solute, and particle transport. Their ability to solve Navier-Stokes, St. Venant, or Darcy equations with closely coupled solute transport and density-dependent flow effects in geometrically complex domains is attractive for inverse modeling of tracer release data and forward modeling of carbon transport in mangrove estuaries under various future conditions. Key physical processes to be simulated include tidal cycles, storm surge, sea level change, variable upstream stage, subsurface groundwater inputs, and precipitation/recharge and their effects on estuary salinity and carbon transport in the estuaries and groundwater beneath the mangroves. Carbon sources and storage in the aquifer and exchanges at the mangrove-estuary interface and carbon transformations in the water column also need to be simulated. Everglades tidal mangrove estuaries are characterized by relatively high velocity (approaching 1 m s-1) tidal flows. The channels are generally less than 2 m in depth. Tidal fluctuations approach 2 m leading to significant areas of periodic inundation and emergence of oyster beds, shell beaches, mangrove root masses, and sandy beaches. Initial models are two-dimensional, although a three-dimensional model explicitly incorporating bathymetry, density-dependent flow, and wind-driven circulation could be developed. Preliminary work highlights some of the abilities of early models. A satellite image of a 64-km2 area surrounding a CO2 flux tower is used to provide the model geometry. Model resolution is 15 m per grid node. A sinusoidal tidal stage variation and constant, high salinity are applied to the Gulf side of the model while a constant stage (corresponding to mean tide), zero salinity boundary is applied on the inland side. The Navier-Stokes equations coupled with the advection-diffusion equation are solved in the open channels. The mangrove areas
Twisted 3D N=4 supersymmetric YM on deformed A{sub 3}{sup *} lattice
Saidi, El Hassan
2014-01-15
We study a class of twisted 3D N=4 supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice L{sub 3D} formally denoted as L{sub 3D}{sup su{sub 3}×u{sub 1}} and given by non-trivial fibration L{sub 1D}{sup u{sub 1}}×L{sub 2D}{sup su{sub 3}} with base L{sub 2D}{sup su{sub 3}}=A{sub 2}{sup *}, the weight lattice of SU(3). We first, develop the twisted 3D N=4 SYM in continuum by using superspace method where the scalar supercharge Q is manifestly exhibited. Then, we show how to engineer the 3D lattice L{sub 3D}{sup su{sub 3}×u{sub 1}} that host this theory. After that we build the lattice action S{sub latt} invariant under the following three points: (i) U(N) gauge invariance, (ii) BRST symmetry, (iii) the S{sub 3} point group symmetry of L{sub 3D}{sup su{sub 3}×u{sub 1}}. Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on L{sub 2D}≡L{sub 2D}{sup su{sub 2}×u{sub 1}}, the extension to twisted maximal 5D SYM with 16 supercharges on lattice L{sub 5D}≡L{sub 5D}{sup su{sub 4}×u{sub 1}} as well as the relation with known results are also given.
The Quantum Dynamics of a Dilute Gas in a 3D BCC Optical Lattice
NASA Astrophysics Data System (ADS)
Reichl, Linda; Boretz, Yingyue
2015-03-01
The classical and quantum dynamics of a dilute gas of rubidium atoms, in a 3D body-centered cubic optical lattice, is studied for a range of polarizations of the laser beams forming the lattice. The relative polarization of the lasers determines the the structure of the potential energy seen by the rubidium atoms. If three pairs of in-phase mutually perpendicular laser beams, with the same wavelength, form the lattice, only a limited range of possible couplings can be realized in the lab. We have determined the band structure of the BCC optical lattice for all theoretically possible couplings, and find that the band structure for lattices realizable in the lab, differs significantly from that expected for a BCC crystal. As coupling is increased, the lattice becomes increasingly chaotic and it becomes possible to produce band structure that has qualitative similarity to a BCC. Welch Foundation
Chen, Yu; Navarro, Laurent; Wang, Yan; Courbebaisse, Guy
2014-01-01
Computed Tomography Angiography (CTA) plays an essential role in the diagnosis, treatment evaluation, and monitoring of cerebral aneurysms. Segmentation of CTA medical images of giant intracranial aneurysms (GIA) provides quantitative measurements of thrombus and aneurysms geometrical characteristics allowing 3D reconstruction. In fact, GIA demonstrated neuroradiological features and propensity of partial or total spontaneous intra-aneurysmal thrombosis generating a thrombus. Despite intensive researches on medical image segmentation, aneurysm (Lumen, Thrombus, and Parent Blood Vessels) segmentation remains as a difficult problem that has not been yet resolved. In this paper, we proposed a Lattice Boltzmann Geodesic Active Contour Method (LBGM) for aneurysm segmentation in CTA images in order to estimate both the volumes of the thrombus and the aneurysm. Although the noise in the CTA images is very strong and the edges of the thrombus are not so different than the surrounding tissues, the aneurysms are segmented effectively. Based on these results, a method using a dome-neck aspect ratio (AR) parameter for the evaluation of the Spontaneous Thrombosis (ST) phenomena demonstrates the promising potentiality of this LBGM for clinical applications. PMID:24077409
Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model
Zhao, Jianlin; Yao, Jun; Zhang, Min; Zhang, Lei; Yang, Yongfei; Sun, Hai; An, Senyou; Li, Aifen
2016-01-01
To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results. PMID:27587293
Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model.
Zhao, Jianlin; Yao, Jun; Zhang, Min; Zhang, Lei; Yang, Yongfei; Sun, Hai; An, Senyou; Li, Aifen
2016-01-01
To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results. PMID:27587293
Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method
Gan, Z. L.; Ishak, M. H. H.; Abdullah, M. Z.; Khor, Soon Fuat
2016-01-01
This paper studies the three dimensional (3D) simulation of fluid flows through the ball grid array (BGA) to replicate the real underfill encapsulation process. The effect of different solder bump arrangements of BGA on the flow front, pressure and velocity of the fluid is investigated. The flow front, pressure and velocity for different time intervals are determined and analyzed for potential problems relating to solder bump damage. The simulation results from Lattice Boltzmann Method (LBM) code will be validated with experimental findings as well as the conventional Finite Volume Method (FVM) code to ensure highly accurate simulation setup. Based on the findings, good agreement can be seen between LBM and FVM simulations as well as the experimental observations. It was shown that only LBM is capable of capturing the micro-voids formation. This study also shows an increasing trend in fluid filling time for BGA with perimeter, middle empty and full orientations. The perimeter orientation has a higher pressure fluid at the middle region of BGA surface compared to middle empty and full orientation. This research would shed new light for a highly accurate simulation of encapsulation process using LBM and help to further increase the reliability of the package produced. PMID:27454872
Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method.
Abas, Aizat; Gan, Z L; Ishak, M H H; Abdullah, M Z; Khor, Soon Fuat
2016-01-01
This paper studies the three dimensional (3D) simulation of fluid flows through the ball grid array (BGA) to replicate the real underfill encapsulation process. The effect of different solder bump arrangements of BGA on the flow front, pressure and velocity of the fluid is investigated. The flow front, pressure and velocity for different time intervals are determined and analyzed for potential problems relating to solder bump damage. The simulation results from Lattice Boltzmann Method (LBM) code will be validated with experimental findings as well as the conventional Finite Volume Method (FVM) code to ensure highly accurate simulation setup. Based on the findings, good agreement can be seen between LBM and FVM simulations as well as the experimental observations. It was shown that only LBM is capable of capturing the micro-voids formation. This study also shows an increasing trend in fluid filling time for BGA with perimeter, middle empty and full orientations. The perimeter orientation has a higher pressure fluid at the middle region of BGA surface compared to middle empty and full orientation. This research would shed new light for a highly accurate simulation of encapsulation process using LBM and help to further increase the reliability of the package produced. PMID:27454872
Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring
NASA Astrophysics Data System (ADS)
Zhang, Rui; Roberts, Tyler; Aranson, Igor S.; de Pablo, Juan J.
2016-02-01
Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.
Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring.
Zhang, Rui; Roberts, Tyler; Aranson, Igor S; de Pablo, Juan J
2016-02-28
Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices. PMID:26931724
Lattice-Boltzmann simulations of three-dimensional fluid flow on a desktop computer.
Brewster, Jeffrey D
2007-04-01
The lattice-Boltzmann (LB) method is a cellular automaton approach to simulating fluid flow with many advantages over conventional methods based on the Navier-Stokes equations. It is conceptually simple, amenable to a wide array of boundary conditions, and can be adapted to handle thermal, density, miscibility, and other effects. The LB approach has been used to model a number of fluid systems of interest to analytical chemists, including chromatography columns, micromixers, and electroosmotic pumps. However, widespread use of this tool has been limited, in part because virtually all large-scale 3D simulations in the literature have been executed on supercomputers. This work demonstrates that such simulations can be executed in reasonable periods of time (hours) on a desktop computer using a cross-platform software package that is easy to learn and use. This package incorporates several improvements that enhance the utility of the LB approach, including an algorithm for speeding common calculations by 2 orders of magnitude and a scheme for handling convection-diffusion equations of interest in electrochemical and surface reaction studies. PMID:17319648
Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method
Cantrell, J Nathan; Inclan, Eric J; Joshi, Abhijit S; Popov, Emilian L; Jain, Prashant K
2012-01-01
This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specific preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.
NASA Astrophysics Data System (ADS)
Geneva, Nicholas; Wang, Lian-Ping
2015-11-01
In the past 25 years, the mesoscopic lattice Boltzmann method (LBM) has become an increasingly popular approach to simulate incompressible flows including turbulent flows. While LBM solves more solution variables compared to the conventional CFD approach based on the macroscopic Navier-Stokes equation, it also offers opportunities for more efficient parallelization. In this talk we will describe several different algorithms that have been developed over the past 10 plus years, which can be used to represent the two core steps of LBM, collision and streaming, more effectively than standard approaches. The application of these algorithms spans LBM simulations ranging from basic channel to particle laden flows. We will cover the essential detail on the implementation of each algorithm for simple 2D flows, to the challenges one faces when using a given algorithm for more complex simulations. The key is to explore the best use of data structure and cache memory. Two basic data structures will be discussed and the importance of effective data storage to maximize a CPU's cache will be addressed. The performance of a 3D turbulent channel flow simulation using these different algorithms and data structures will be compared along with important hardware related issues.
Increasing the filling of ultracold KRb molecules in a 3D optical lattice
NASA Astrophysics Data System (ADS)
Moses, Steven; Covey, Jacob; Gadway, Bryce; Yan, Bo; Miecnikowski, Matthew; Ye, Jun; Jin, Deborah
2015-05-01
Ultracold polar molecules, with their long-range electric dipolar interactions, offer new opportunities for studying quantum magnetism and many-body physics. Recently, our group observed spin exchange interactions between KRb molecules in a 3D optical lattice, which is one of the first steps towards studying lattice spin models with polar molecules. The lattice fillings were about 10% or less in these experiments. Future experiments will benefit greatly from lower entropies and higher lattice fillings. Here, we have investigated the molecular creation process in a 3D optical lattice with the goal of maximizing the filling fraction. We start by loading a BEC of Rb and a degenerate Fermi gas of K into a 3D optical lattice. In the absence of K, Rb is a Mott insulator. We study how the Mott insulator and the filling of Rb are affected by the presence of K and develop a strategy to maintain high Rb filling throughout the molecule production process. We also find that we can convert a large fraction of these Rb to molecules when we operate with low Rb numbers. We acknowledge funding from DARPA, DOE, NIST, NSF, AFOSR, and the NDSEG Graduate Fellowship.
Boltzmann Fluctuations in Numerical Simulations of Nonequilibrium Lattice Threshold Systems
Rundle, J.B.; Klein, W.; Gross, S.; Turcotte, D.L.
1995-08-21
Nonequilibrium threshold systems such as slider blocks are now used to model a variety of dynamical systems, including earthquake faults, driven neural networks, and sliding charge density waves. We show that for general mean field models driven at low rates fluctuations in the internal energy field are characterized by Boltzmann statistics. Numerical simulations confirm this prediction. Our results indicate that mean field models can be effectively treated as equilibrium systems.
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-06-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.
Pore-scale discretisation limits of multiphase lattice-Boltzmann methods
NASA Astrophysics Data System (ADS)
Li, Z.; Middleton, J.; Varslot, T.; Sheppard, A.
2015-12-01
Lattice-Boltzmann (LB) modeling is a popular method for the numerical solution of the Navier-Stokes equations and several multi-component LB models are widely used to simulate immiscible two-phase fluid flow in porous media. However, there has been relatively little study of the models' ability to make optimal use of 3D imagery by considering the minimum number of grid points that are needed to represent geometric features such as pore throats. This is of critical importance since 3D images of geological samples are a compromise between resolution and field of view. In this work we explore the discretisation limits of LB models, their behavior near these limits, and the consequences of this behavior for simulations of drainage and imbibition. We quantify the performance of two commonly used multiphase LB models: Shan-Chen (SC) and Rothman-Keller (RK) models in a set of tests, including simulations of bubbles in bulk fluid, on flat surfaces, confined in flat/tilted tubes, and fluid invasion into single tubes. Simple geometries like these allow better quantification of model behavior and better understanding of breakdown mechanisms. In bulk fluid, bubble radii less than 2.5 grid units (image voxels) cause numerical instability in SC model; the RK model is stable to a radius of 2.5 units and below, but with poor agreement with the Laplace's law. When confined to a flat duct, the SC model can simulate similar radii to RK model, but with higher interface spurious currents than the RK model and some risk of instability. In tilted ducts with 'staircase' voxel-level roughness, the SC model seems to average the roughness, whereas for RK model only the 'peaks' of the surface are relevant. Overall, our results suggest that LB models can simulate fluid capillary pressure corresponding to interfacial radii of just 1.5 grid units, with the RK model exhibiting significantly better stability.
Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability
NASA Astrophysics Data System (ADS)
Liang, H.; Li, Q. X.; Shi, B. C.; Chai, Z. H.
2016-03-01
In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number (At=0.15 ) in a long square duct (12 W ×W ×W ) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002), 10.1103/PhysRevLett.88.134502]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009), 10.1103/PhysRevE.80.055302] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011), 10.1063/1.3555523]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost.
Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability.
Liang, H; Li, Q X; Shi, B C; Chai, Z H
2016-03-01
In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number (A(t)=0.15) in a long square duct (12W × W × W) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009)] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011)]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost. PMID:27078453
NASA Astrophysics Data System (ADS)
Brogi, F.; Malaspinas, O.; Bonadonna, C.; Chopard, B.; Ripepe, M.
2015-12-01
Low frequency (< 20Hz) acoustic measurements have a great potential for the real time characterization of volcanic plume source parameters. Using the classical source theory, acoustic data can be related to the exit velocity of the volcanic jet and to mass eruption rate, based on the geometric constrain of the vent and the mixture density. However, the application of the classical acoustic source models to volcanic explosive eruptions has shown to be challenging and a better knowledge of the link between the acoustic radiation and actual volcanic fluid dynamics processes is required. New insights into this subject could be given by the study of realistic aeroacoustic numerical simulations of a volcanic jet. Lattice Boltzmann strategies (LBS) provide the opportunity to develop an accurate, computationally fast, 3D physical model for a volcanic jet. In the field of aeroacoustic applications, dedicated LBS has been proven to have the low dissipative properties needed for capturing the weak acoustic pressure fluctuations. However, due to the big disparity in magnitude between the flow and the acoustic disturbances, even weak spurious noise sources in simulations can ruin the accuracy of the acoustic predictions. Reflected waves from artificial boundaries defined around the flow region can have significant influence on the flow field and overwhelm the acoustic field of interest. In addition, for highly multiscale turbulent flows, such as volcanic plumes, the number of grid points needed to represent the smallest scales might become intractable and the most complicated physics happen only in small portions of the computational domain. The implementation of the grid refinement, in our model allow us to insert local finer grids only where is actually needed and to increase the size of the computational domain for running more realistic simulations. 3D LBS model simulations for turbulent jet aeroacoustics have been accurately validated. Both mean flow and acoustic results
The lattice Boltzmann model for the second-order Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2010-04-01
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin-Ono equation. With the Taylor expansion and the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations.
Topology optimization in thermal-fluid flow using the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Yaji, Kentaro; Yamada, Takayuki; Yoshino, Masato; Matsumoto, Toshiro; Izui, Kazuhiro; Nishiwaki, Shinji
2016-02-01
This paper proposes a topology optimization method for thermal-fluid flow problems using the lattice Boltzmann method (LBM). The design sensitivities are derived based on the adjoint lattice Boltzmann method (ALBM), whose basic idea is that the adjoint problem is first formulated using a continuous adjoint approach, and the adjoint problem is then solved using the LBM. In this paper, the discrete velocity Boltzmann equation, in which only the particle velocities are discretized, is introduced to the ALBM to deal with the various boundary conditions in the LBM. The novel sensitivity analysis is applied in two flow channel topology optimization problems: 1) a pressure drop minimization problem, and 2) a heat exchange maximization problem. Several numerical examples are provided to confirm the utility of the proposed method.
Developing extensible lattice-Boltzmann simulationsfor general-purpose graphics-programming units
Walsh, S C; Saar, M O
2011-10-27
Lattice-Boltzmann methods are versatile numerical modeling techniques capable of reproducing a wide variety of fluid-mechanical behavior. These methods are well suited to parallel implementation, particularly on the single-instruction multiple data (SIMD) parallel processing environments found in computer graphics processing units (GPUs). Although more recent programming tools dramatically improve the ease with which GPU programs can be written, the programming environment still lacks the flexibility available to more traditional CPU programs. In particular, it may be difficult to develop modular and extensible programs that require variable on-device functionality with current GPU architectures. This paper describes a process of automatic code generation that overcomes these difficulties for lattice-Boltzmann simulations. It details the development of GPU-based modules for an extensible lattice-Boltzmann simulation package - LBHydra. The performance of the automatically generated code is compared to equivalent purpose written codes for both single-phase, multiple-phase, and multiple-component flows. The flexibility of the new method is demonstrated by simulating a rising, dissolving droplet in a porous medium with user generated lattice-Boltzmann models and subroutines.
Developing extensible lattice-Boltzmann simulators for general-purpose graphics-processing units
Walsh, S C; Saar, M O
2011-12-21
Lattice-Boltzmann methods are versatile numerical modeling techniques capable of reproducing a wide variety of fluid-mechanical behavior. These methods are well suited to parallel implementation, particularly on the single-instruction multiple data (SIMD) parallel processing environments found in computer graphics processing units (GPUs). Although more recent programming tools dramatically improve the ease with which GPU programs can be written, the programming environment still lacks the flexibility available to more traditional CPU programs. In particular, it may be difficult to develop modular and extensible programs that require variable on-device functionality with current GPU architectures. This paper describes a process of automatic code generation that overcomes these difficulties for lattice-Boltzmann simulations. It details the development of GPU-based modules for an extensible lattice-Boltzmann simulation package - LBHydra. The performance of the automatically generated code is compared to equivalent purpose written codes for both single-phase, multiple-phase, and multiple-component flows. The flexibility of the new method is demonstrated by simulating a rising, dissolving droplet in a porous medium with user generated lattice-Boltzmann models and subroutines.
Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows
NASA Astrophysics Data System (ADS)
Prestininzi, Pietro; Montessori, Andrea; La Rocca, Michele; Succi, Sauro
2016-09-01
It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.
Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure
NASA Astrophysics Data System (ADS)
Shi, Wei; Lu, Wei-Zhen; Xue, Yu; He, Hong-Di
2016-02-01
A revised lattice Boltzmann model concerning the equilibrium traffic pressure is proposed in this study to tackle the phase transition phenomena of traffic flow system. The traditional lattice Boltzmann model has limitation to investigate the complex traffic phase transitions due to its difficulty for modeling the equilibrium velocity distribution. Concerning this drawback, the equilibrium traffic pressure is taken into account to derive the equilibrium velocity distribution in the revised lattice Boltzmann model. In the proposed model, a three-dimensional velocity-space is assumed to determine the equilibrium velocity distribution functions and an alternative, new derivative approach is introduced to deduct the macroscopic equations with the first-order accuracy level from the lattice Boltzmann model. Based on the linear stability theory, the stability conditions of the corresponding macroscopic equations can be obtained. The outputs indicate that the stability curve is divided into three regions, i.e., the stable region, the neutral stability region, and the unstable region. In the stable region, small disturbance appears in the initial uniform flow and will vanish after long term evolution, while in the unstable region, the disturbance will be enlarged and finally leads to the traffic system entering the congested state. In the neutral stability region, small disturbance does not vanish with time and maintains its amplitude in the traffic system. Conclusively, the stability of traffic system is found to be enhanced as the equilibrium traffic pressure increases. Finally, the numerical outputs of the proposed model are found to be consistent with the recognized, theoretical results.
NASA Technical Reports Server (NTRS)
Menon, Suresh
2003-01-01
This report summarizes the progress made in the first 8 to 9 months of this research. The Lattice Boltzmann Equation (LBE) methodology for Large-eddy Simulations (LES) of microblowing has been validated using a jet-in-crossflow test configuration. In this study, the flow intake is also simulated to allow the interaction to occur naturally. The Lattice Boltzmann Equation Large-eddy Simulations (LBELES) approach is capable of capturing not only the flow features associated with the flow, such as hairpin vortices and recirculation behind the jet, but also is able to show better agreement with experiments when compared to previous RANS predictions. The LBELES is shown to be computationally very efficient and therefore, a viable method for simulating the injection process. Two strategies have been developed to simulate multi-hole injection process as in the experiment. In order to allow natural interaction between the injected fluid and the primary stream, the flow intakes for all the holes have to be simulated. The LBE method is computationally efficient but is still 3D in nature and therefore, there may be some computational penalty. In order to study a large number or holes, a new 1D subgrid model has been developed that will simulate a reduced form of the Navier-Stokes equation in these holes.
NASA Astrophysics Data System (ADS)
Wong, T.; Sun, W.
2012-12-01
Microcomputed tomography can be used to characterize the geometry of the pore space of a sedimentary rock, with resolution that is sufficiently refined for the realistic simulation of physical properties based on the 3D image. Significant advances have been made on the characterization of pore size distribution and connectivity, development of techniques such as lattice Boltzmann method to simulate permeability, and its upscaling. Sun, Andrade and Rudnicki (2011) recently introduced a multiscale method that dynamically links these three aspects, which were often treated separately in previous computational schemes. In this study, we improve the efficiency of this multiscale method by introducing a flood-fill algorithm to determine connectivity of the pores, followed by a multiscale lattice Boltzmann/finite element calculation to obtain homogenized effective anisotropic permeability. The improved multiscale method also includes new capacity to consistently determine electrical conductivity and formation factor from CT images. Furthermore, we also introduce a level set based method that transforms pore geometry to finite element mesh and thus enables direct simulation of pore-scale flow with finite element method. When applied to the microCT data acquired by Lindquist et al. (2000) for four Fontainebleau sandstone samples with porosities ranging from 7.5% to 22%, this multiscale method has proved to be computationally efficient and our simulations has provided new insights into the relation among permeability, pore geometry and connectivity.
Loading mode dependent effective properties of octet-truss lattice structures using 3D-printing
NASA Astrophysics Data System (ADS)
Challapalli, Adithya
Cellular materials, often called lattice materials, are increasingly receiving attention for their ultralight structures with high specific strength, excellent impact absorption, acoustic insulation, heat dissipation media and compact heat exchangers. In alignment with emerging additive manufacturing (AM) technology, realization of the structural applications of the lattice materials appears to be becoming faster. Considering the direction dependent material properties of the products with AM, by directionally dependent printing resolution, effective moduli of lattice structures appear to be directionally dependent. In this paper, a constitutive model of a lattice structure, which is an octet-truss with a base material having an orthotropic material property considering AM is developed. In a case study, polyjet based 3D printing material having an orthotropic property with a 9% difference in the principal direction provides difference in the axial and shear moduli in the octet-truss by 2.3 and 4.6%. Experimental validation for the effective properties of a 3D printed octet-truss is done for uniaxial tension and compression test. The theoretical value based on the micro-buckling of truss member are used to estimate the failure strength. Modulus value appears a little overestimate compared with the experiment. Finite element (FE) simulations for uniaxial compression and tension of octettruss lattice materials are conducted. New effective properties for the octet-truss lattice structure are developed considering the observed behavior of the octet-truss structure under macroscopic compression and tension trough simulations.
Increasing the filling fraction of ultracold polar KRb molecules in a 3D optical lattice
NASA Astrophysics Data System (ADS)
Moses, Steven; Gadway, Bryce; Yan, Bo; Covey, Jacob; Jin, Deborah; Ye, Jun
2013-05-01
Gases of ultracold polar molecules with sufficiently low entropy are an ideal experimental scenario to look for signatures of long-range many-body interactions. Having a high filling fraction in a 3D lattice is one way to achieve a low entropy state. In earlier work, we showed that preformed pairs of K and Rb in a 3D lattice (sites that have exactly one K and one Rb) are converted to KRb Feshbach molecules with nearly 100% efficiency. Since the STIRAP transfer from Feshbach molecules to ground-state molecules is 90-100% efficient, loading a 3D lattice with a large fraction of preformed pairs will lead to a large filling fraction of ground-state molecules. Our scheme is to load a Mott insulator of Rb and band insulator of K. After we have loaded a lattice with a high filling fraction, we will investigate effects of dipolar interactions in a many-body system. We acknowledge funding from NIST, NSF, AFOSR-MURI, and the NDSEG Graduate Fellowship.
Lattice-Boltzmann simulation of laser interaction with weakly ionized helium plasmas
Li Huayu; Ki, Hyungson
2010-07-15
This paper presents a lattice Boltzmann method for laser interaction with weakly ionized plasmas considering electron impact ionization and three-body recombination. To simulate with physical properties of plasmas, the authors' previous work on the rescaling of variables is employed and the electromagnetic fields are calculated from the Maxwell equations by using the finite-difference time-domain method. To calculate temperature fields, energy equations are derived separately from the Boltzmann equations. In this way, we attempt to solve the full governing equations for plasma dynamics. With the developed model, the continuous-wave CO{sub 2} laser interaction with helium is simulated successfully.
NASA Astrophysics Data System (ADS)
Chen, Lin-Jie; Ma, Chang-Feng
2010-01-01
This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.
Lin, X.
1991-01-01
This paper reports the development of an object-oriented programming methodology for particle simulations. It is established on the (m reductionist) view that many physical phenomena cana be reduced to many-body problems. By doing the reduction, many seemly unrelated physical phenomena can be simulated in a systematic way and a high-level programming system can be constructed to facilitate the programming and the solution of the simulations. In the object-oriented particle simulation methodology, a hierarchy of abstract particles is defined to represent a variety of characteristics in physical system simulations. A simulation program is constructed from particles derived from the abstract particles. The object- oriented particle simulation methodology provides a unifying modeling and simulation framework for a variety of simulation applications with the use of particle methods. It allows easy composition of simulation programs from predefined software modules and facilitates software reusability. It greatly increase the productivity of simulation program constructions. Boltzmann (after Ludwig Boltzmann, 1844-1906) is a prototype programming system in the object-oriented particle simulation methodology. Boltzmann is implemented in C++ and the X Window System. It contains a library of data types and functions that support simulations in particle methods. Moreover, it provides a visualization window to support friendly user-computer interaction. Examples of the application of the Boltzmann programming system are presented. The effectiveness of the object-oriented particle simulation methodology is demonstrated. A user's manual is included in the appendix.
Finite-difference lattice Boltzmann simulation on acoustics-induced particle deposition
NASA Astrophysics Data System (ADS)
Fu, Sau-Chung; Yuen, Wai-Tung; Wu, Chili; Chao, Christopher Yu-Hang
2015-10-01
Particle manipulation by acoustics has been investigated for many years. By a proper design, particle deposition can be induced by the same principle. The use of acoustics can potentially be developed into an energy-efficient technique for particle removal or filtration system as the pressure drop due to acoustic effects is low and the flow velocity is not necessary to be high. Two nonlinear acoustic effects, acoustic streaming and acoustic radiation pressure, are important. Acoustic streaming introduces vortices and stagnation points on the surface of an air duct and removes the particles by deposition. Acoustic radiation pressure causes particles to form agglomerates and enhances inertial impaction and/or gravitational sedimentation. The objective of this paper is to develop a numerical model to investigate the particle deposition induced by acoustic effects. A three-step approach is adopted and lattice Boltzamnn technique is employed as the numerical method. This is because the lattice Boltzmann equation is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. In the first step, the acoustic field and its mean square fluctuation values are calculated. Due to the advantage of the lattice Boltzmann technique, a simple, stable and fast lattice Boltzmann method is proposed and verified. The result of the first step is input into the second step to solve for acoustic streaming. Another finite difference lattice Boltzmann method, which has been validated by a number of flows and benchmark cases in the literature, is used. The third step consists in tracking the particle's motion by a Lagrangian approach where the acoustic radiation pressure is considered. The influence of the acoustics effects on particle deposition is explained. The numerical result matches with an experiment. The model is a useful tool for optimizing the design and helps to further develop the technique.
Lattice-Boltzmann simulation of coalescence-driven island coarsening
Basagaoglu, H.; Green, C.T.; Meakin, P.; McCoy, B.J.
2004-01-01
The first-order phase separation in a thin fluid film was simulated using a two-dimensional lattice-Boltzman model (LBM) with fluid-fluid interactions. The effects of the domain size on the intermediate asymptotic island size distribution were also discussed. It was observed that the overall process is dominated by coalescence which is independent of island mass. The results show that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations.
Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model.
Zhou, Changjun; Hou, Caixia; Zhang, Qiang; Wei, Xiaopeng
2013-09-01
The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences. PMID:23824509
Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange.
Giovacchini, Juan P; Ortiz, Omar E
2015-12-01
We review the momentum exchange method to compute the flow force and torque on a submerged body in lattice-Boltzmann methods by presenting an alternative derivation. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface, and it relies on general principles. After the introduction of the momentum exchange method in lattice-Boltzmann methods, some formulations were introduced to compute the fluid force on static and moving bodies. These formulations were introduced in a rather intuitive, ad hoc way. In our derivation, we recover the proposals most frequently used, in some cases with minor corrections, gaining some insight into the two most used formulations. At the end, we present some numerical tests to compare different approaches on a well-known benchmark test that support the correctness of the formulas derived. PMID:26764848
Conservative phase-field lattice Boltzmann model for interface tracking equation.
Geier, Martin; Fakhari, Abbas; Lee, Taehun
2015-06-01
Based on the phase-field theory, we propose a conservative lattice Boltzmann method to track the interface between two different fluids. The presented model recovers the conservative phase-field equation and conserves mass locally and globally. Two entirely different approaches are used to calculate the gradient of the phase field, which is needed in computation of the normal to the interface. One approach uses finite-difference stencils similar to many existing lattice Boltzmann models for tracking the two-phase interface, while the other one invokes central moments to calculate the gradient of the phase field without any finite differences involved. The former approach suffers from the nonlocality of the collision operator while the latter is entirely local making it highly suitable for massive parallel implementation. Several benchmark problems are carried out to assess the accuracy and stability of the proposed model. PMID:26172824
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
NASA Astrophysics Data System (ADS)
Held, M.; Kendl, A.
2015-10-01
A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.
NASA Astrophysics Data System (ADS)
Ding, E. J.
2015-06-01
The time-independent lattice Boltzmann algorithm (TILBA) is developed to calculate the hydrodynamic interactions between two particles in a Stokes flow. The TILBA is distinguished from the traditional lattice Boltzmann method in that a background matrix (BGM) is generated prior to the calculation. The BGM, once prepared, can be reused for calculations for different scenarios, and the computational cost for each such calculation will be significantly reduced. The advantage of the TILBA is that it is easy to code and can be applied to any particle shape without complicated implementation, and the computational cost is independent of the shape of the particle. The TILBA is validated and shown to be accurate by comparing calculation results obtained from the TILBA to analytical or numerical solutions for certain problems.
Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions
NASA Astrophysics Data System (ADS)
Chen, Yu; Cai, Qingdong; Xia, Zhenhua; Wang, Moran; Chen, Shiyi
2013-07-01
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.
NASA Astrophysics Data System (ADS)
Obliger, Amaël; Duvail, Magali; Jardat, Marie; Coelho, Daniel; Békri, Samir; Rotenberg, Benjamin
2013-07-01
We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.
NASA Astrophysics Data System (ADS)
Kang, XiuYing; Su, YanPing
2012-10-01
Cross-flows around two, three and four circular cylinders in tandem, side-by-side, isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5 D, where D is the identical circular cylinder diameter. The wake patterns, pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases. The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures, which are interesting, complex and useful for practical applications. This study provides a useful database to validate the simplicity, accuracy and robustness of the Lattice Boltzmann method.
Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange
NASA Astrophysics Data System (ADS)
Giovacchini, Juan P.; Ortiz, Omar E.
2015-12-01
We review the momentum exchange method to compute the flow force and torque on a submerged body in lattice-Boltzmann methods by presenting an alternative derivation. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface, and it relies on general principles. After the introduction of the momentum exchange method in lattice-Boltzmann methods, some formulations were introduced to compute the fluid force on static and moving bodies. These formulations were introduced in a rather intuitive, ad hoc way. In our derivation, we recover the proposals most frequently used, in some cases with minor corrections, gaining some insight into the two most used formulations. At the end, we present some numerical tests to compare different approaches on a well-known benchmark test that support the correctness of the formulas derived.
Regularized lattice Boltzmann model for a class of convection-diffusion equations.
Wang, Lei; Shi, Baochang; Chai, Zhenhua
2015-10-01
In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. PMID:26565368
Prediction of sound absorption in rigid porous media with the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric
2016-02-01
In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.
Rossby vortex simulation on a paraboloidal coordinate system using the lattice Boltzmann method.
Yu, H; Zhao, K
2001-11-01
In this paper, we apply our compressible lattice Boltzmann model to a rotating parabolic coordinate system to simulate Rossby vortices emerging in a layer of shallow water flowing zonally in a rotating paraboloidal vessel. By introducing a scaling factor, nonuniform curvilinear mesh can be mapped to a flat uniform mesh and then normal lattice Boltzmann method works. Since the mass per unit area on the two-dimensional (2D) surface varies with the thickness of the water layer, the 2D flow seems to be "compressible" and our compressible model is applied. Simulation solutions meet with the experimental observations qualitatively. Based on this research, quantitative solutions and many natural phenomena simulations in planetary atmospheres, oceans, and magnetized plasma, such as the famous Jovian Giant Red Spot, the Galactic Spiral-vortex, the Gulf Stream, and the Kuroshio Current, etc., can be expected. PMID:11736137
A study of multiphase flow in fractured porous media using a microscale lattice Boltzmann approach
Soll, W.E.; Eggert, K.E.; Grunau, D.W.; Schafer-Perini, A.L.
1994-02-01
The lattice Boltzmann technique has been shown to be an efficient and reliable approach to modeling single- and multi-fluid flow in porous media systems. The flexibility of this approach in discretizing the pore/solid space means it is particularly well suited to capturing fluid behavior, fluid-fluid interactions, and fluid-solid interactions at the scale of the individual pores. Such flexibility readily lends itself to studying processes occurring at physical interfaces, such as between a fracture and the surrounding porous matrix. Here we present pore-level simulations of fluid flow through a fracture embedded in an unsaturated matrix. Simulations are run on the massively parallel Connection Machine 5 (CM-5) using the two-fluid, two-dimensional lattice Boltzmann flow simulator developed at Los Alamos National Laboratory. We look at the effect of pressure gradients and initial matrix saturation on infiltration into the matrix and fluid flow along the fracture.
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles.
Ramachandran, S; Sunil Kumar, P B; Pagonabarraga, I
2006-06-01
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution. PMID:16779527
A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
NASA Astrophysics Data System (ADS)
Ramachandran, S.; Kumar, P. B. Sunil; Pagonabarraga, I.
2006-06-01
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.
Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method
NASA Technical Reports Server (NTRS)
Chen, Hudong; Chen, Shiyi; Matthaeus, William H.
1992-01-01
A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.
On the lattice Boltzmann method for multiphase flows with large density ratios
NASA Astrophysics Data System (ADS)
Kim, Seung Hyun; Pitsch, Heinz
2015-12-01
An analysis of the lattice Boltzmann (LB) method for multiphase flows with large density ratios is presented. It is shown that for incompressible, multiphase LB methods, the divergence-free condition is not satisfied within the formal accuracy of the LB method, when the density ratio between the two phases is large enough. The discrete differentiation-by-parts rule is responsible for this error. A new multiphase LB method to resolve this issue is proposed.
Entropic Lattice Boltzmann Methods for Fluid Mechanics: Thermal, Multi-phase and Turbulence
NASA Astrophysics Data System (ADS)
Chikatamarla, Shyam; Boesch, F.; Frapolli, N.; Mazloomi, A.; Karlin, I.
2014-11-01
With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques. Major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence. In this talk, we shall review recent advances in ELBM as a practical, modeling-free tool for simulation of complex flow phenomenon. We shall present recent simulations of fluid turbulence including turbulent channel flow, flow past a circular cylinder, creation and dynamics of vortex tubes, and flow past a surface mounted cube. Apart from its achievements in turbulent flow simulations, ELBM has also presented us the opportunity to extend lattice Boltzmann method to higher order lattices which shall be employed for turbulent, multi-phase and thermal flow simulations. A new class of entropy functions are proposed to handle non-ideal equation of state and surface tension terms in multi-phase flows. It is shown the entropy principle brings unconditional stability and thermodynamic consistency to all the three flow regimes considered here. Acknowledgements: ERC Advanced Grant ``ELBM'' and CSCS grant s437 are deeply acknowledged. References:
Modeling flue pipes: Subsonic flow, lattice Boltzmann, and parallel distributed computers
NASA Astrophysics Data System (ADS)
Skordos, Panayotis A.
1995-01-01
The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial-viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80 percent parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts.
Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications
NASA Astrophysics Data System (ADS)
Wu, J.; Shu, C.
2009-04-01
A version of immersed boundary-lattice Boltzmann method (IB-LBM) is proposed in this work. It is based on the lattice Boltzmann equation with external forcing term proposed by Guo et al. [Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65 (2002) 046308], which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect. In this model, the velocity is contributed by two parts. One is from the density distribution function and can be termed as intermediate velocity, and the other is from the external force and can be considered as velocity correction. In the conventional IB-LBM, the force density (external force) is explicitly computed in advance. As a result, we cannot manipulate the velocity correction to enforce the non-slip boundary condition at the boundary point. In the present work, the velocity corrections (force density) at all boundary points are considered as unknowns which are computed in such a way that the non-slip boundary condition at the boundary points is enforced. The solution procedure of present IB-LBM is exactly the same as the conventional IB-LBM except that the non-slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model. Numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results. This is not the case for the results obtained by the conventional IB-LBM. Another advantage of the present method is its simple calculation of force on the boundary. The force can be directly calculated from the relationship between the velocity correction and the force density.
Design of Chern and Mott insulators in buckled 3 d oxide honeycomb lattices
NASA Astrophysics Data System (ADS)
Doennig, David; Baidya, Santu; Pickett, Warren E.; Pentcheva, Rossitza
2016-04-01
Perovskite (La X O3 )2/(LaAlO3)4(111) superlattices with X spanning the entire 3 d transition-metal series combine the strongly correlated, multiorbital nature of electrons in transition-metal oxides with a honeycomb lattice as a key feature. Based on density functional theory calculations including strong interaction effects, we establish trends in the evolution of electronic states as a function of several control parameters: band filling, interaction strength, spin-orbit coupling (SOC), and lattice instabilities. Competition between local pseudocubic and global trigonal symmetry as well as the additional flexibility provided by the magnetic and spin degrees of freedom of 3 d ions lead to a broad array of distinctive broken-symmetry ground states not accessible for the (001)-growth direction, offering a platform to design two-dimensional electronic functionalities. Constraining the symmetry between the two triangular sublattices causes X =Mn , Co, and Ti to emerge as Chern insulators driven by SOC. For X =Mn we illustrate how interaction strength and lattice distortions can tune these systems between a Dirac semimetal, a Chern and a trivial Mott insulator.
NASA Astrophysics Data System (ADS)
Xia, Yong; Lu, De-Tang; Liu, Yang; Xu, You-Sheng
2009-03-01
The multiple-relaxation-time lattice Boltzmann method (MRT-LBM) is implemented to numerically simulate the cross flow over a longitudinal vibrating circular cylinder. This research is carried out on a three-dimensional (3D) finite cantilevered cylinder to investigate the effect of forced vibration on the wake characteristics and the 3D effect of a cantilevered cylinder. To meet the accuracy of this method, the present calculation is carried out at a low Reynolds number Re = 100, as well as to make the vibration obvious, we make the vibration strong enough. The calculation results indicate that the vibration has significant influence on the wake characteristics. When the vibrating is big enough, our early works show that the 2D vortex shedding would be locked up by vibration. Contrarily, this phenomenon would not appear in the present 3D case because of the end effect of the cantilevered cylinder.
NASA Astrophysics Data System (ADS)
Zhang, Jianying; Yan, Guangwu; Wang, Moran
2016-02-01
A lattice Boltzmann model for solving the three-dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Differently from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a three-dimensional space, and the evolution of the model is about a spatial axis rather than time. The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Examples show that the model accurately reproduces the vortex tori pattern in the CQCGLE.
Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer
NASA Astrophysics Data System (ADS)
Shi, Yong; Yap, Ying Wan; Sader, John E.
2015-07-01
Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.
Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.
Shi, Yong; Yap, Ying Wan; Sader, John E
2015-07-01
Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales. PMID:26274307
Zu, Y Q; He, S
2013-04-01
A lattice Boltzmann model (LBM) is proposed based on the phase-field theory to simulate incompressible binary fluids with density and viscosity contrasts. Unlike many existing diffuse interface models which are limited to density matched binary fluids, the proposed model is capable of dealing with binary fluids with moderate density ratios. A new strategy for projecting the phase field to the viscosity field is proposed on the basis of the continuity of viscosity flux. The new LBM utilizes two lattice Boltzmann equations (LBEs): one for the interface tracking and the other for solving the hydrodynamic properties. The LBE for interface tracking can recover the Chan-Hilliard equation without any additional terms; while the LBE for hydrodynamic properties can recover the exact form of the divergence-free incompressible Navier-Stokes equations avoiding spurious interfacial forces. A series of 2D and 3D benchmark tests have been conducted for validation, which include a rigid-body rotation, stationary and moving droplets, a spinodal decomposition, a buoyancy-driven bubbly flow, a layered Poiseuille flow, and the Rayleigh-Taylor instability. It is shown that the proposed method can track the interface with high accuracy and stability and can significantly and systematically reduce the parasitic current across the interface. Comparisons with momentum-based models indicate that the newly proposed velocity-based model can better satisfy the incompressible condition in the flow fields, and eliminate or reduce the velocity fluctuations in the higher-pressure-gradient region and, therefore, achieve a better numerical stability. In addition, the test of a layered Poiseuille flow demonstrates that the proposed scheme for mixture viscosity performs significantly better than the traditional mixture viscosity methods. PMID:23679542
NASA Astrophysics Data System (ADS)
Zu, Y. Q.; He, S.
2013-04-01
A lattice Boltzmann model (LBM) is proposed based on the phase-field theory to simulate incompressible binary fluids with density and viscosity contrasts. Unlike many existing diffuse interface models which are limited to density matched binary fluids, the proposed model is capable of dealing with binary fluids with moderate density ratios. A new strategy for projecting the phase field to the viscosity field is proposed on the basis of the continuity of viscosity flux. The new LBM utilizes two lattice Boltzmann equations (LBEs): one for the interface tracking and the other for solving the hydrodynamic properties. The LBE for interface tracking can recover the Chan-Hilliard equation without any additional terms; while the LBE for hydrodynamic properties can recover the exact form of the divergence-free incompressible Navier-Stokes equations avoiding spurious interfacial forces. A series of 2D and 3D benchmark tests have been conducted for validation, which include a rigid-body rotation, stationary and moving droplets, a spinodal decomposition, a buoyancy-driven bubbly flow, a layered Poiseuille flow, and the Rayleigh-Taylor instability. It is shown that the proposed method can track the interface with high accuracy and stability and can significantly and systematically reduce the parasitic current across the interface. Comparisons with momentum-based models indicate that the newly proposed velocity-based model can better satisfy the incompressible condition in the flow fields, and eliminate or reduce the velocity fluctuations in the higher-pressure-gradient region and, therefore, achieve a better numerical stability. In addition, the test of a layered Poiseuille flow demonstrates that the proposed scheme for mixture viscosity performs significantly better than the traditional mixture viscosity methods.
The sign-factor of the 3D Ising model on dual BCC lattice
NASA Astrophysics Data System (ADS)
Khachatryan, Sh.; Sedrakyan, A.
2002-01-01
We modify the two-dimensional model for the sign-factor of the regular 3D Ising model (3DIM) presented by Kavalov and Sedrakyan (Phys. Lett. 173B (1986) 449 and Nucl. Phys. 285B (1987) 264) for the case of dual to body centered cubic (DBCC) three-dimensional lattice. The advantage of this lattice is in an absence of self-intersections of the two-dimensional surfaces embedded there. We investigate simpler case of the model with scalar fermions (instead of SU(2) needed for 3DIM) and have found it's spectrum, which appeared to be massless. We reformulate the model by use of R-matrix formalism and a new interesting structure appears in a necessity to introduce three-particle R(3)ijk-matrices. We formulate the integrability property of the model for more general case.
Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge Theory
Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko
2005-06-03
We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED{sub 3} and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.
Lattice Boltzmann simulation of electrostatic double layer interaction force for nanoparticles
NASA Astrophysics Data System (ADS)
Shi, Grace X.; Jin, Yan; Lazouskaya, Volha; Wang, Chao; Wang, Lian-Ping
2011-11-01
Modeling the transport and retention of nanoparticles (NPs) through soil porous media requires an accurate description of the electrostatic interaction force between a nanoparticle and soil grain. In this study, we apply the lattice Boltzmann method to directly solve the nonlinear Poisson Boltzmann (PB) equation for several geometric configurations including plate-plate, NP-plate, and NP-NP interactions, for any surface potentials and interaction distances and for different boundary conditions. Interaction energy and force are then derived from the simulations. For the case of plate-plate interaction, the simulation results are compared to the exact solution of the nonlinear PB equation. It is shown that the linear PB solution is valid when the nondimensional surface potential is less than one, and that the linear PB solution over-predicts the interaction force for intermediate gap distances but under-predicts the force for small gap distances. For NP-plate and NP-NP interactions, an axisymmetric lattice Boltzmann formulation is developed to solve the governing equations. The results will be compared to the classic approximate expressions of interaction force to evaluate their validity and to study the effect of nanoparticle size. Work supported by NSF and USDA.
Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions.
Lallemand, Pierre; Luo, Li-Shi
2003-09-01
The focus of the present work is to provide an analysis for the acoustic and thermal properties of the energy-conserving lattice Boltzmann models, and a solution to the numerical defects and instability associated with these models in two and three dimensions. We discover that a spurious algebraic coupling between the shear and energy modes of the linearized evolution operator is a defect universal to the energy-conserving Boltzmann models in two and three dimensions. This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann equation: (1) its simple spatial-temporal dynamics, (2) the linearity of the relaxation modeling for collision operator, and (3) the energy-conservation constraint. To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equation (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time model due to d'Humières, whereas the diffusion-advection equation for the temperature is solved separately by using finite-difference technique (or other means). Through the Chapman-Enskog analysis we show that the hydrodynamic equations derived from the proposed HTLBE model include the equivalent effect of gamma=C(P)/C(V) in both the speed and attenuation of sound. Appropriate coupling between the energy and velocity field is introduced to attain correct acoustics in the model. The numerical stability of the HTLBE scheme is analyzed by solving the dispersion equation of the linearized collision operator. We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed. It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids. We also present
Discovery of a 3d-transition-metal-based ferromagnetic Kondo lattice system
NASA Astrophysics Data System (ADS)
Us Saleheen, Ahmad; Samanta, Tapas; Lepkowski, Daniel; Shankar, Alok; Prestigiacomo, Joseph; Dubenko, Igor; Quetz, Abdiel; McDougald, Roy, Jr.; McCandless, Gregory; Chan, Julia; Adams, Philip; Young, David; Ali, Naushad; Stadler, Shane
2015-03-01
The formation of a Kondo lattice results in a wide variety of exotic phenomena associated with the competition between the Kondo effect and the RKKY interaction, such as heavy fermions, non-Fermi liquid behavior, unconventional superconductivity, and so on. A quantum critical point (QCP) has been frequently observed at the boundaries of competing phases for antiferromagnetic materials. However, the existence of a ferromagnetic (FM) QCP is unclear. Moreover, FM Kondo lattices are rare. Here we report the discovery of a FM Kondo lattice system Mn1-xFexCoGe, which is the first example of a 3d-metal-based system (i.e., not rare-earth-based). Resistivity, magnetic susceptibility, heat capacity and thermopower studies on a single crystal sample indicate that the anisotropic FM kondo lattice has formed along c-axis. The signature of a spin density wave transition was also observed above the Kondo minimum, below which the resistivity follows a log(T) behavior. This work was supported by the U.S. Department of Energy (Grant Nos. DE-FG02-13ER46946 and DE-FG02-06ER46291).
NASA Astrophysics Data System (ADS)
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2014-05-01
We study the coupling between hydraulic and electric flows in a porous medium at small scale using the Lattice Boltzmann method. This method is a computational fluid dynamics technique that is used for advection and diffusion modeling. We implement a coupled Lattice Boltzmann algorithm that solves both the mass transport and the electric field arising from charges displacements. The streaming potential and electroosmosis phenomena occur in a variety of situations and derive from this coupling. We focus on the streaming potential which is described using the ratio between the created potential difference and the applied pressure gradient. The streaming potential is assumed to be a linear function of the fluid conductivity, but experimental results highlight anomalous behaviors at low and high salinity. We try to account for them by setting extreme conditions that are likely to generate non-linearities. Several pore radii are tested so as to determine what is the effect of a radius that is comparable to the Debye length, the screening length of the electric potential, due to the ions in the electrolyte. The volumetric integral of the electrical current is calculated for comparison with the 2D simulations. High values of zeta potential are tested to verify if the discrepancy regarding the theoretical result is concentration-dependent. We try to include a surface conductivity term in the coefficient formulation. Some tests including a rugosity on the channel walls are performed. All of these attempts show a normal behaviour of the streaming potential at high salinity. We observe a decrease of the ratio at low conductivity, showing that this ratio is modified when the pore radius becomes negligible compared with the Debye length, which is physically meaningful in little pores at low concentrations. References : S. Pride. Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50 : 15678-15696, 1994. D. A. Wolf
Boundary conditions of the lattice Boltzmann method for convection-diffusion equations
NASA Astrophysics Data System (ADS)
Huang, Juntao; Yong, Wen-An
2015-11-01
In this paper, we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice Boltzmann method for convection-diffusion equations with general Robin boundary conditions. One scheme is for straight boundaries, with the boundary points locating at any distance from the lattice nodes, and has second-order accuracy. The other is for curved boundaries, has only first-order accuracy and is much simpler than the existing schemes. Unlike those in the literature, our schemes involve only the current lattice node. Such a "single-node" boundary schemes are highly desirable for problems with complex geometries. The two schemes are validated numerically with a number of examples. The numerical results show the utility of the constructed schemes and very well support our theoretical predications.
Lattice Boltzmann technique for heat transport phenomena coupled with melting process
NASA Astrophysics Data System (ADS)
Ibrahem, A. M.; El-Amin, M. F.; Mohammadein, A. A.; Gorla, Rama Subba Reddy
2016-04-01
In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar-Gross-Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.
Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids.
Horbach, J; Frenkel, D
2001-12-01
We present a simulation scheme based on the lattice-Boltzmann method to simulate the dynamics of charged colloids in an electrolyte. In our model we describe the electrostatics on the level of a Poisson-Boltzmann equation and the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We verify our simulation scheme by means of a Chapman-Enskog expansion. Our method is applied to the calculation of the reduced sedimentation velocity U/U(0) for a cubic array of charged spheres in an electrolyte. We show that we recover the analytical solution first derived by Booth [F. Booth, J. Chem. Phys. 22, 1956 (1954)] for a weakly charged, isolated sphere in an unbounded electrolyte. The present method makes it possible to go beyond the Booth theory, and we discuss the dependence of the sedimentation velocity on the charge of the spheres. Finally we compare our results to experimental data. PMID:11736191
Radiative or neutron transport modeling using a lattice Boltzmann equation framework
NASA Astrophysics Data System (ADS)
Bindra, H.; Patil, D. V.
2012-07-01
In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.
Evaluation of the Performance of the Hybrid Lattice Boltzmann Based Numerical Flux
NASA Astrophysics Data System (ADS)
Zheng, H. W.; Shu, C.
2016-06-01
It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko
2014-04-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials. PMID:24827360
NASA Astrophysics Data System (ADS)
Boutra, Abdelkader; Ragui, Karim; Bennacer, Rachid; Benkahla, Youb K.
2016-05-01
In this paper, we investigate numerically the 3D dimensional laminar flow of an incompressible Newtonian fluid into a rectangular channel, including several blocks mounted on the lower and upper walls. To do so, a numerical code based on the lattice Boltzmann method is utilized and it has been validated after comparison between the present results and those of the literature. The adiabatic partitions are arranged in three different manners: in the first one; and by using two blocks, these latter are mounted the one against the other. In the second, the bottom block is disposed next to the flow entry. Whereas, in the third; three parallel (or alternative) blocks are taking place the one close to the other at an equal distance. Regarding the Reynolds number and the partitions' distance effects on the fluid flow inside the channel, our phenomenon is widely analyzed throughout streamlines and velocity profiles, with special attention to the partitions' arrangement and the global drop pressure. It is to denote that the three dimensions D3Q19 model is adopted in this work, based on a cubic lattice, where each pattern of the latter is characterized by nineteen discrete speeds. Contribution to the topical issue "Materials for Energy Harvesting, Conversion and Storage (ICOME 2015) - Elected submissions", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui
Simulation Study of Micro Particles Behavior in Fluid Flow Using Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Miyoshi, T.; Yamada, Y.; Matsuoka, T.
2004-12-01
Evaluation of underground hydraulic characteristics has been a key issue not only for hydrogeology but for various fields of geo-engineering. We have been investigating hydraulic properties, such as permeability, of fractures and porous rocks using a 3D lattice Boltzmann method (LBM) for recent several years. In this paper, we propose a coupling method of LBM and DEM (distinct element method) to incorporate dynamic interaction of fluid flow and particles. This coupling technique brings new insights into the effect of micro particles in the hydraulic properties, such that migration and sedimentation of solid particles remarkably decreases permeability. We present two simulation examples; I) sedimentation of micro particles by the gravity in dead water, II) behaviour of micro particles in fluid flow through a porous media. In the simulation-I, surface geometry of the particle assembly shows a gentle 'sag' with a subtle subsidence at its center, suggesting that the upward fluid expulsion causes slightly uplifted geometry. Such geometry of particles can be commonly seen in natural sedimentary rocks that deformed due to fluid expulsion at its unconsolidated stages. The simulation-II clearly showed some conditions of pore throat plugging by the micro particles. The fluid flow pattern should be significantly affected by the moving particles, as well as the pressure difference (an input parameter). The percolation distance of solid particles was well controlled with the pressure difference and throat geometries. We concluded that the coupling simulation of LBM and DEM has extremely high potential to investigate the behavior of solid and fluid interactions. The technique can simulate permeability changes precisely, that are affected by dynamic or physical factors such as compaction. Fluid flow simulations with the technique can be directly applied for plugging of solid particles within a reservoir, which is significant for petroleum production and drill-hole completion. The
Theory and lattice Boltzmann simulations of rapidly oscillating flows: Application to nanofluidics
NASA Astrophysics Data System (ADS)
Colosqui, Carlos Esteban
This dissertation investigates oscillating flows of simple fluids in a wide range of frequency and density variation. Understanding these flows is of fundamental importance for state-of-the-art engineering applications such as nano/microelectromechanical systems (N/MEMS) operating in diverse fluidic environments. A fluid weakly perturbed from thermodynamic equilibrium relaxes back to equilibrium state on a time scale tau ˜lambda/ cs. In the low frequency limit tauo << 1 a predominantly viscous behavior is accurately predicted by the Navier-Stokes equations. We demonstrate that in the high-frequency limit tauo >> 1 a novel transition to viscoelastic flow occurs. The viscoelastic flow of simple fluids is mathematically described via analytical solution of the Boltzmann-BGK equation of kinetic gas theory. Theoretically predicted phenomena are numerically simulated via kinetic-based approaches (i.e. high-order lattice Boltzmann methods) and observed in physical experiments with nanomechanical resonators operating over a wide pressure (10-1 ≤ p ≤ 103torr) and frequency range (103 ≤ o ≤ 108sec-1). The principal results of this dissertation are: (1) We state that the limit tauo >> 1 of high-frequency flows is governed by a damped-wave equation (i.e. the telegraph equation); (2) A universal function for the energy dissipation rate in the entire range of frequency and pressure variation is derived and favorably compared against experimental and numerical data; (3) The derived extended hydrodynamic description predicts a novel viscoelastic transition of simple fluids that holds fundamental importance from both scientific and technological standpoints. (4) We prove that high-order lattice Boltzmann schemes employing finite Hermite expansions of the Boltzmann distribution and proper regularization procedures can accurately represent macroscopic physics of the investigated flows. (5) Qualitative and quantitative agreement between theory, simulation and experiment
New spiral state and skyrmion lattice in 3D model of chiral magnets
NASA Astrophysics Data System (ADS)
Rybakov, Filipp N.; Borisov, Aleksandr B.; Blügel, Stefan; Kiselev, Nikolai S.
2016-04-01
We present the phase diagram of magnetic states for films of isotropic chiral magnets (ChMs) calculated as function of applied magnetic field and thickness of the film. We have found a novel magnetic state driven by the natural confinement of the crystal, localized at the surface and stacked on top of the conical bulk phase. This magnetic surface state has a three-dimensional (3D) chiral spin-texture described by the superposition of helical and cycloidal spin spirals. This surface state exists for a large range of applied magnetic fields and for any film thickness beyond a critical one. We also identified the whole thickness and field range for which the skyrmion lattice becomes the ground state of the system. Below a certain critical thickness the surface state and bulk conical phase are suppressed in favor of the skyrmion lattice. Unraveling of those phases and the construction of the phase diagram became possible using advanced computational techniques for direct energy minimization applied to a basic 3D model for ChMs. Presented results provide a comprehensive theoretical description for those effects already observed in experiments on thin films of ChMs, predict new effects important for applications and open perspectives for experimental studies of such systems.
Ji, Chenzhen; Zhao, Dan
2014-06-01
In this work, three-dimensional numerical simulations of acoustically excited flow through a millimeter-size circular orifice are conducted to assess its noise damping performance, with particular emphasis on applying the lattice Boltzmann method (LBM) as an alternative computational aeroacoustics tool. The model is intended to solve the discrete lattice Boltzmann equation (LBE) by using the pseudo-particle based technique. The LBE controls the particles associated with collision and propagation over a discrete lattice mesh. Flow variables such as pressure, density, momentum, and internal energy are determined by performing a local integration of the particle distribution at each time step. This is different from the conventional numerical investigation attempting to solve Navier-Stokes (NS) equations by using high order finite-difference or finite-volume methods. Compared with the conventional NS solvers, one of the main advantages of LBM may be a reduced computational cost. Unlike frequency domain simulations, the present investigation is conducted in time domain, and the orifice damping behavior is quantified over a broad frequency range at a time by forcing an oscillating flow with multiple tones. Comparing the numerical results with those obtained from the theoretical models, large eddy simulation, and experimental measurements, good agreement is observed. PMID:24907789
A conservative Dirichlet boundary treatment for the finite volume lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Chen, Leitao; Schaefer, Laura
2014-11-01
The finite volume lattice Boltzmann method (FVLBM) enables the model to use the exact body-fitting mesh in the flow problems that involve the complex boundaries. However, the development of proper boundary treatment for the FVLBM has been outpaced. The boundary treatments designed for the conventional lattice Boltzmann method (LBM) framework are still heavily applied to the FVLBM. The largest defect of using the old boundary treatment is that, on the Dirichlet boundaries, the macroscopic variables cannot be conserved. In another word, there exist nontrivial discrepancies between the macroscopic variables defined by the boundary conditions and those yield by the numerical solutions. The errors on the boundaries will contaminate the internal solutions and even cause instability, especially on the complex boundaries. To overcome such a shortcoming, a conservative boundary treatment for the Dirichlet hydrodynamic boundary conditions is developed for the FVLBM. Through the benchmark tests, it is shown that the macroscopic conservations on the Direchlet boundaries are up to machine accuracy and completely independent of the size of relaxation time, the type of lattice model, the level of mesh resolution, the shape of boundaries and the type of internal scheme.
Lattice Boltzmann methods for some 2-D nonlinear diffusion equations:Computational results
Elton, B.H.; Rodrigue, G.H. . Dept. of Applied Science Lawrence Livermore National Lab., CA ); Levermore, C.D. . Dept. of Mathematics)
1990-01-01
In this paper we examine two lattice Boltzmann methods (that are a derivative of lattice gas methods) for computing solutions to two two-dimensional nonlinear diffusion equations of the form {partial derivative}/{partial derivative}t u = v ({partial derivative}/{partial derivative}x D(u){partial derivative}/{partial derivative}x u + {partial derivative}/{partial derivative}y D(u){partial derivative}/{partial derivative}y u), where u = u({rvec x},t), {rvec x} {element of} R{sup 2}, v is a constant, and D(u) is a nonlinear term that arises from a Chapman-Enskog asymptotic expansion. In particular, we provide computational evidence supporting recent results showing that the methods are second order convergent (in the L{sub 1}-norm), conservative, conditionally monotone finite difference methods. Solutions computed via the lattice Boltzmann methods are compared with those computed by other explicit, second order, conservative, monotone finite difference methods. Results are reported for both the L{sub 1}- and L{sub {infinity}}-norms.
NASA Astrophysics Data System (ADS)
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2015-04-01
Streaming-potentials are produced by electrokinetic effects in relation to fluid flow, and are used for geophysical prospecting. The electrokinetic coupling is induced by the coupling between the fluid flow and the electrical flow, which results from the presence of an electrical double layer at the rock/pore water interface. When fluid flows through a porous medium, it gives rise to an electric streaming current, counterbalanced by a conduction current, leading to a resulting measurable electrical voltage. Streaming current generation is well understood in water-saturated porous media, but the streaming potential coefficient at very-low and very-high salinities can show a non-linear behaviour. The aim of this study is to model the streaming potential coefficient using Lattice Boltzmann simulations and to quantify the effect of parameters such as fluid conductivity and rugosity. The lattice Boltzmann method is computational fluid dynamics technique that allows to solve advection and diffusion phenomena. We implement a coupled lattice Boltzmann algorithm that solves both the flow in a rock channel and the electrical diffusion to calculate the streaming potential coefficient (ratio between the created potential difference and the applied pressure gradient) in various situations. In this study, we aim at quantifying the change that is brought by taking into account the dependence of the local fluid conductivity on the local concentration. We also observe the influence of a rough surface on the behaviour of this coefficient with the fluid salinity. We try to generate non-linearities regarding the theoretical prediction of the streaming potential coefficient with a view to explaining existing experimental measurements.
Modeling Flue Pipes: Subsonic Flow, Lattice Boltzmann, and Parallel Distributed Computers.
NASA Astrophysics Data System (ADS)
Skordos, Panayotis A.
1995-01-01
The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder, the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial -viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80% parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).
Design of Mott and topological phases on buckled 3d-oxide honeycomb lattices
NASA Astrophysics Data System (ADS)
Pentcheva, Rossitza
The honeycomb lattice, as realized e.g. in graphene, has rendered a robust platform for innovative science and potential applications. A much richer generalization of this lattice arises in (111)-oriented bilayers of perovskites, adding the complexity of the strongly correlated, multiorbital nature of electrons in transition metal oxides. Based on first principles calculations with an on-site Coulomb repulsion, here we provide trends in the evolution of ground states versus band filling in (111)-oriented (La XO3)2 /(LaAlO3)4 superlattices, with X spanning the entire 3d transition metal series. The competition between local quasi-cubic and global triangular symmetry triggers unanticipated broken symmetry phases, with mechanisms ranging from Jahn-Teller distortion, to charge-, spin-, and orbital-ordering. LaMnO3 and LaCoO3 bilayers, where spin-orbit coupling opens a sizable gap in the Dirac-point Fermi surface, emerge as much desired oxide-based Chern insulators, the latter displaying a gap capable of supporting room-temperature applications Further realizations of the honeycomb lattice and geometry patterns beyond the perovskite structure will be addressed. Research supported by the DFG, SFB/TR80.
Lattice Boltzmann Simulations of Blood Flow: Non-Newtonian Rheology and Clotting Processes
NASA Astrophysics Data System (ADS)
Ouared, Rafik; Chopard, Bastien
2005-10-01
The numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent. In this paper, we consider a Lattice Boltzmann (LB) approach to bloodflow modeling and we implement a non-Newtonian correction in order to reproduce more realistic flow profiles. We obtain a good agreement between simulations and Casson's model of blood rheology in a simple geometry. Finally we discuss how, by using a passive scalar suspension model with aggregation on top of the LB dynamics, we can describe the clotting processes in the aneurysm
Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles
NASA Astrophysics Data System (ADS)
Semprebon, Ciro; Krüger, Timm; Kusumaatmaja, Halim
2016-03-01
We present a ternary free-energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model presented here can be extended to include an arbitrary number of fluid components.
Topology optimization of unsteady flow problems using the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Nørgaard, Sebastian; Sigmund, Ole; Lazarov, Boyan
2016-02-01
This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.
Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas
NASA Astrophysics Data System (ADS)
Brewer, Jasmine; Mendoza, Miller; Young, Ryan E.; Romatschke, Paul
2016-01-01
We present fully nonlinear dissipative fluid dynamics simulations of a strongly interacting trapped two-dimensional Fermi gas using a lattice Boltzmann algorithm. We are able to simulate nonharmonic trapping potentials, temperature-dependent viscosities, as well as a discretized version of the ballistic (noninteracting) behavior. Our approach lends itself to direct comparison with experimental data, opening up the possibility of a precision determination of transport coefficients in the strongly interacting Fermi gas. Furthermore, we predict the presence of a strongly damped ("nonhydrodynamic") component in the quadrupole mode, which should be observable experimentally.
NASA Astrophysics Data System (ADS)
Riaud, Antoine; Zhao, Shufang; Wang, Kai; Cheng, Yi; Luo, Guangsheng
2014-05-01
Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds.
Volumetric Lattice Boltzmann Simulation for Fluid dynamics and Turbulence in Practical Syringes
NASA Astrophysics Data System (ADS)
Lima, Everton; Deep, Debanjan; Yu, Huidan (Whitney)
2012-11-01
We conduct numerical experiments to study fluid dynamics and turbulence in syringes using volumetric lattice Boltzmann method (VLBM) that is developed for dealing with arbitrary moving boundaries. Several common used medical syringes are used to predict the efficiency and safety of syringes experiencing low flow infusion rates. It is found that smaller size syringes reach a steady flow rate much sooner than larger ones, which are in quantitative agreement with experimental results. The relation between the syringe size and its steady flow rate is revealed. At low flow rates, corner vortices are observed. We explore conditions that lead to turbulent flow aiming to aid safer syringe application in nursing practices.
Porous Substrate Effects on Thermal Flows Through a Rev-Scale Finite Volume Lattice Boltzmann Model
NASA Astrophysics Data System (ADS)
Zarghami, Ahad; Francesco, Silvia Di; Biscarini, Chiara
2014-09-01
In this paper, fluid flows with enhanced heat transfer in porous channels are investigated through a stable finite volume (FV) formulation of the thermal lattice Boltzmann method (LBM). Temperature field is tracked through a double distribution function (DDF) model, while the porous media is modeled using Brinkman-Forchheimer assumptions. The method is tested against flows in channels partially filled with porous media and parametric studies are conducted to evaluate the effects of various parameters, highlighting their influence on the thermo-hydrodynamic behavior.
GPU phase-field lattice Boltzmann simulations of growth and motion of a binary alloy dendrite
NASA Astrophysics Data System (ADS)
Takaki, T.; Rojas, R.; Ohno, M.; Shimokawabe, T.; Aoki, T.
2015-06-01
A GPU code has been developed for a phase-field lattice Boltzmann (PFLB) method, which can simulate the dendritic growth with motion of solids in a dilute binary alloy melt. The GPU accelerated PFLB method has been implemented using CUDA C. The equiaxed dendritic growth in a shear flow and settling condition have been simulated by the developed GPU code. It has been confirmed that the PFLB simulations were efficiently accelerated by introducing the GPU computation. The characteristic dendrite morphologies which depend on the melt flow and the motion of the dendrite could also be confirmed by the simulations.
Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows
NASA Technical Reports Server (NTRS)
Luo, Li-Shi; Qi, Dewei; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.
Effect of Rolling Massage on the Vortex Flow in Blood Vessels with Lattice Boltzmann Simulation
NASA Astrophysics Data System (ADS)
Yi, Hou Hui
The rolling massage manipulation is a classic Chinese Medical Massage, which is a nature therapy in eliminating many diseases. Here, the effect of the rolling massage on the cavity flows in blood vessel under the rolling manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the vortex flows are fully disturbed by the rolling massage. The flow behavior depends on the rolling velocity and the rolling depth. Rolling massage has a better effect on the flows in the cavity than that of the flows in a planar blood vessel. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.
Simulation of residual oil displacement in a sinusoidal channel with the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Otomo, Hiroshi; Fan, Hongli; Hazlett, Randy; Li, Yong; Staroselsky, Ilya; Zhang, Raoyang; Chen, Hudong
2015-10-01
We simulate oil slug displacement in a sinusoidal channel in order to validate computational models and algorithms for multi-component flow. This case fits in the gap between fully realistic cases characterized by complicated geometry and academic cases with simplistic geometry. Our computational model is based on the lattice Boltzmann method and allows for variation of physical parameters such as wettability and viscosity. The effect of variation of model parameters is analyzed, in particular via comparison with analytical solutions. We discuss the requirements for accurate solution of the oil slug displacement problem.
Application of lattice Boltzmann method for analysis of underwater vortex dynamics
NASA Astrophysics Data System (ADS)
Nuraiman, Dian; Viridi, Sparisoma; Purqon, Acep
2015-09-01
Vortex dynamics is one of problems arising in fluid dynamics. Vortices are a major characteristic of turbulent flow. We perform the Lattice Boltzmann Method (LBM) with Bhatnagar-Gross-Krook (BGK) approximation to analyze the underwater vortex dynamics close to the shoreline. Additionally, the Smagorinsky tubulence model is applied to treat turbulent flow and a special method for free surface treatment is applied to overcome free surface. Furthermore, we investigate the effect of the turbulence factor and the seabed profile to vortex dynamics. The results show a smaller turbulence factor affected to more turbulent flow and coral reefs reduced movement of vortex towards the shoreline.
NASA Astrophysics Data System (ADS)
Jung, Narina; Seo, Hae Won; Yoo, Chun Sang
2015-12-01
Two-dimensional (2-D) characteristic boundary conditions (CBC) based on the characteristic analysis are formulated for the lattice Boltzmann methods (LBM). In this approach, the classical locally-one dimensional inviscid (LODI) relations are improved by recovering multi-dimensional effects on flows at open boundaries. The 2-D CBC are extended to a general subsonic flow configuration in the LBM and the effects of the transverse terms are clarified. From the vortex convection and vortex shedding problems, it is verified that the improved CBC shows better performance in accuracy compared to the conventional CBC approaches.
Riaud, Antoine; Zhao, Shufang; Wang, Kai; Cheng, Yi; Luo, Guangsheng
2014-05-01
Despite the popularity of the lattice-Boltzmann method (LBM) in simulating multiphase flows, a general approach for modeling dilute species in multiphase systems is still missing. In this report we propose to modify the collision operator of the solute by introducing a modified redistribution scheme. This operator is based on local fluid variables and keeps the parallelism inherent to LBM. After deriving macroscopic transport equations, an analytical equation of state of the solute is exhibited and the method is proven constituting a unified framework to simulate arbitrary solute distribution between phases, including single-phase soluble compounds, amphiphilic species with a partition coefficient, and surface-adsorbed compounds. PMID:25353915
Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar
2014-01-01
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. PMID:24688360
Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar
2014-01-01
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. PMID:24688360
NASA Astrophysics Data System (ADS)
Guo, Pengfei; Guan, Yong; Liu, Gang; Liang, Zhiting; Liu, Jianhong; Zhang, Xiaobo; Xiong, Ying; Tian, Yangchao
2016-09-01
This work reports an investigation of the impact of microstructure on the performance of solid oxide fuel cells (SOFC) composed of nickel yttria-stabilized zirconia (Ni YSZ). X-ray nano computed tomography (nano-CT) was used to obtain three-dimensional (3D) models of Ni-YSZ composite anode samples subjected to different thermal cycles. Key parameters, such as triple phase boundary (TPB) density, were calculated using 3D reconstructions. The electrochemical reaction occurring at active-TPB was modeled by the Lattice Boltzmann Method for simulation of multi-component mass transfer in porous anodes. The effect of different electrode geometries on the mass transfer and the electrochemical reaction in anodes was studied by TPB distributions measured by nano CT for samples subjected to different thermal cycles. The concentration polarization and the activation polarization were estimated respectively. The results demonstrate that a combined approach involving nano-CT experiments in conjunction with simulations of gas transport and electrochemical reactions using the Lattice Boltzmann method can be used to better understand the relationship between electrode microstructure and performance of nickel yttria-stabilized zirconia anodes.
NASA Astrophysics Data System (ADS)
Wang, Y.; Shu, C.; Yang, L. M.
2015-12-01
An improved multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this work for effective simulation of three-dimensional (3D) multiphase flows with large density ratio and high Reynolds number. As a finite volume scheme, the MLBFS originally proposed in [27] applies the finite volume method to solve for macroscopic flow variables directly. The fluxes are reconstructed locally at each cell interface by using the standard LBM solutions. Due to the modeling error of the standard LBM, the reconstructed fluxes deviate from those in the Navier-Stokes equations; and to compensate this error, a complex tensor is introduced in the original MLBFS. However, the computation of the tensor introduces additional complexity and usually needs a relatively thicker interface thickness to maintain numerical stability, which makes the solver be complex and inefficient in the 3D case. To remove this drawback, in this work, a theoretical analysis to the formulations obtained from the Chapman-Enskog expansion is conducted. It is shown that the modeling error can be effectively removed by modifying the computation of the equilibrium density distribution function. With this improvement, the proposed 3D MLBFS not only avoids the calculation of the compensation tensor but also is able to maintain numerical stability with very thin interface thickness. Several benchmark cases, including the challenging droplet impacting on a dry surface, head-on collisions of binary droplets and droplet splashing on a thin film with density ratio 1000 and Reynolds number up to 3000, are studied to validate the proposed solver. The obtained results agree well with the published data.
Multiple-relaxation-time lattice Boltzmann simulations of turbulent channel and pipe flows.
NASA Astrophysics Data System (ADS)
Opadrishta, Harish; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The mesoscopic Lattice Boltzmann method (LBM) has become a reliable alternative for solving incompressible turbulent flows. However, the statistics of a simulated turbulent flow near a curved boundary may deviate from the physical rotational invariance (RI) of lattice coordinates. The main objective of this study is to compare the effects of different lattice models on the simulation results of turbulent flows, and explore ways to restore RI near a curved boundary. We will apply D3Q19 and D3Q27 multiple-relaxation-time LBM models to simulate turbulent pipe and channel flows. The statistics of the simulated flows are examined to quantify the nature of departures from RI. To help understand whether the departure is originated from the bounce-back scheme at the solid wall, we will perform simulations of a turbulent channel flow with walls orientated at an angle from the lattice grid, and test the use of an overset lattice grid near a pipe wall. The Chapman-Enskog analysis of these models will be performed to probe RI errors near a boundary. Our goal is to eventually perform an accurate direct numerical simulation of a turbulent pipe flow, and compare the results to previous simulations based on the Navier-Stokes equations.
Application of the multicomponent lattice Boltzmann simulation method to oil/water dispersions
NASA Astrophysics Data System (ADS)
Seaton, M. A.; Halliday, I.; Masters, A. J.
2011-03-01
We study the propagation of acoustic fields in bounded, two-dimensional, mono-disperse oil/water emulsions using a carefully modified and appropriately calibrated single relaxation time multicomponent lattice Boltzmann equation simulation. Our model is a variant of an algorithm applying both interface forces based on macroscopic surface tensions and a kinematic condition for phase separation, adapted to allow sonic speed variations between its oil and water components. Appropriate second-order accurate acoustic boundary conditions are obtained from a node-based lattice closure with local mass conservation and applicability for varying fluid viscosities. Data from an example simulation of a single oil drop in water interacting with a generated standing acoustic wave are presented and, where appropriate, compared with empirical theories and analogous calculations for a solid object.
NASA Astrophysics Data System (ADS)
Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping
2014-04-01
The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing absorbing and scattering media with graded index subjected to a short square laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. Firstly, for the case of the refractive index matched boundary, LBM solutions to transient radiative transfer in graded index medium are validated by comparison with results reported in the literature. Afterward, LBM is employed to investigate transient radiative transfer in graded index medium with a refractive index discontinuity at the boundaries. Effects of the graded index distributions, the optical thickness, and scattering phase function on transmittance and reflectance signals are investigated, and several interesting trends on the time-resolved signals are observed and analyzed.
Amoeboid migration mode adaption in quasi-3D spatial density gradients of varying lattice geometry
NASA Astrophysics Data System (ADS)
Gorelashvili, Mari; Emmert, Martin; Hodeck, Kai F.; Heinrich, Doris
2014-07-01
Cell migration processes are controlled by sensitive interaction with external cues such as topographic structures of the cell’s environment. Here, we present systematically controlled assays to investigate the specific effects of spatial density and local geometry of topographic structure on amoeboid migration of Dictyostelium discoideum cells. This is realized by well-controlled fabrication of quasi-3D pillar fields exhibiting a systematic variation of inter-pillar distance and pillar lattice geometry. By time-resolved local mean-squared displacement analysis of amoeboid migration, we can extract motility parameters in order to elucidate the details of amoeboid migration mechanisms and consolidate them in a two-state contact-controlled motility model, distinguishing directed and random phases. Specifically, we find that directed pillar-to-pillar runs are found preferably in high pillar density regions, and cells in directed motion states sense pillars as attractive topographic stimuli. In contrast, cell motion in random probing states is inhibited by high pillar density, where pillars act as obstacles for cell motion. In a gradient spatial density, these mechanisms lead to topographic guidance of cells, with a general trend towards a regime of inter-pillar spacing close to the cell diameter. In locally anisotropic pillar environments, cell migration is often found to be damped due to competing attraction by different pillars in close proximity and due to lack of other potential stimuli in the vicinity of the cell. Further, we demonstrate topographic cell guidance reflecting the lattice geometry of the quasi-3D environment by distinct preferences in migration direction. Our findings allow to specifically control amoeboid cell migration by purely topographic effects and thus, to induce active cell guidance. These tools hold prospects for medical applications like improved wound treatment, or invasion assays for immune cells.
NASA Astrophysics Data System (ADS)
Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.
2016-04-01
In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.
Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation
NASA Astrophysics Data System (ADS)
Frapolli, N.; Chikatamarla, S. S.; Karlin, I. V.
2016-06-01
We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015), 10.1103/PhysRevE.92.061301]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry.
Simulation of three-component fluid flows using the multiphase lattice Boltzmann flux solver
NASA Astrophysics Data System (ADS)
Shi, Y.; Tang, G. H.; Wang, Y.
2016-06-01
In this work, we extend the multiphase lattice Boltzmann flux solver, which was proposed in [1] for simulating incompressible flows of binary fluids based on two-component Cahn-Hilliard model, to three-component fluid flows. In the present method, the multiphase lattice Boltzmann flux solver is applied to solve for the flow field and the three-component Cahn-Hilliard model is used to predict the evolution of the interfaces. The proposed method is first validated through the classical problem of simulation of partial spreading of a liquid lens between the other two components. Numerical results of interface shapes and contact angles agree well with theoretical solutions. After that, to further demonstrate the capability of the present method, several numerical examples of three-component fluid flows are presented, including a bubble rising across a fluid-fluid interface, single droplet falling through a fluid-fluid interface, the collision-coalescence of two droplets, and the non-contact collision of two droplets. It is shown that the present method can successfully handle complex interactions among three components.
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.
Liu, Haihu; Valocchi, Albert J; Zhang, Yonghao; Kang, Qinjun
2013-01-01
A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions. PMID:23410429
NASA Astrophysics Data System (ADS)
Marenduzzo, D.; Orlandini, E.; Cates, M. E.; Yeomans, J. M.
2007-09-01
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently “extensile” rods, in the case of flow-aligning liquid crystals, and for sufficiently “contractile” ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of “convection rolls.” These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics.
Developing the R&D 100 award-winning lattice Boltzmann permeameter toward a marketable product
Soll, W.E.; Chen, Shi-Yi; Doolen, G.D.; Eggert, K.G.
1996-11-01
This is the final report of a one-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Computational models of oil, gas, and water flow through porous reservoir rock are used in reservoir management to decide whether or not, and how, to develop and produce hydrocarbon reserves. The flow models have major impact on these decisions so their accuracy, cost, and speed is paramount. The accuracy of the flow models is strongly dependent on the accuracy of the physical characterization of the reservoir rock`s pore-fluid system. System characterization is typically done in the laboratory. As an alternative, we have developed a numerical approach for determining the constitutive information. The project sought to use computational techniques that could incorporate all of the basic physical processes that influence fluid movement through the porous rock yet remain computationally efficient. The lattice Boltzmann (LB) numerical technique fits these requirements, and is able to incorporate complex pore geometries exactly and reproduce behavior of multiple fluids. The flexibility of the LB approach allows the numerical model, called the lattice Boltzmann Permeameter (LBP), to determine constitutive relationships (i.e., relative permeabilities) over a much wider range of conditions than can be achieved in a laboratory. Our project was directed toward improving the LBP to make it available to a wide range of users. Improvements were made in computational speed and efficiency, user interfaces, and visualization capabilities.
Marenduzzo, D; Orlandini, E; Cates, M E; Yeomans, J M
2007-09-01
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently "extensile" rods, in the case of flow-aligning liquid crystals, and for sufficiently "contractile" ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of "convection rolls." These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics. PMID:17930285
Lattice-Boltzmann Simulations of Flows Over Backward-Facing Inclined Steps
NASA Astrophysics Data System (ADS)
Kotapati, Rupesh B.; Shock, Richard; Chen, Hudong
2014-01-01
The lattice-Boltzmann method (LBM) is used in conjunction with a very large-eddy simulation (VLES) turbulence modeling approach to compute separated flows over backward-facing steps at different wall inclination angles. The Reynolds number ReH based on the step height H and center-line velocity at the channel inlet ucl is 64 000. The expansion ratio of the outlet section to the inlet section of the channel is 1.48. Wall inclination angles α considered include 10°, 15°, 20°, 25°, 30° and 90°. The computed flow fields for different inclination angles of the step are assessed against the laser Doppler anemometry (LDA) measurements of Makiola [B. Makiola, Ph.D. Thesis, University of Karlsruhe (1992); B. Ruck and B. Makiola, Flow separation over the step with inclined walls, in Near-Wall Turbulent Flows, eds. R. M. C. So, C. G. Speziale and B. E. Launder (Elsevier, 1993), p. 999.]. In addition to validating the lattice-Boltzmann solution with the experiments, this study also investigates the effects of three dimensionality, the proximity of the inlet to the step, and the grid resolution on the quality of the predictions.
Obliger, Amaël; Duvail, Magali; Jardat, Marie; Coelho, Daniel; Békri, Samir; Rotenberg, Benjamin
2013-07-01
We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations. PMID:23944561
Unstructured Lattice Boltzmann methods for efficient simulation of flow in complex porous media
NASA Astrophysics Data System (ADS)
Mathiesen, Joachim; Mitsztal, Marek; Matin, Rastin; Hernandez, Anier
2015-04-01
The flow permeability of porous rock is the critical control parameter for a number of natural processes in the upper crust. On the pore scale, fluid dynamic simulations are efficient and accurate for determining the flow permeability, while on larger scales where multiple pores are connected in complex networks, the simulations quickly become computationally infeasible. In contrast to flow in open space, porous flow is determined predominantly by the pore geometry. One limiting factor in the computations is the geometrical representation of the pore space. For example, the lattice Boltzmann method, which is often used in direct numerical simulations of flow, is usually implemented using regular cubic grids. Irregular grids, however, allow for a more efficient geometrical representation of space limited by complex boundaries. Here we briefly go through some of the recent advances and advantages of the lattice Boltzmann method on unstructured grids. We briefly discuss basic numerical implementations on the unstructured grids. We show simulations and permeability estimates of flow in real samples of the pore space of chalk.
NASA Astrophysics Data System (ADS)
Zhang, Rui; Roberts, Tyler; de Pablo, Juan; dePablo Team
2014-11-01
Liquid crystals (LC) posses anisotropic viscoelastic properties, and, as such, LC flow can be incredibly complicated. Here we employ a hybrid lattice Boltzmann method (pioneered by Deniston, Yeomans and Cates) to systematically study the hydrodynamics of nematic liquid crystals (LCs) with and without solid particles. This method evolves the velocity field through lattice Boltzmann and the LC-order parameter via a finite-difference solver of the Beris-Edwards equation. The evolution equation of the boundary points with finite anchoring is obtained through Poisson bracket formulation. Our method has been validated by matching the Ericksen-Leslie theory. We demonstrate two applications in the flow alignment regime. We first investigate a hybrid channel flow in which the top and bottom walls have different anchoring directions. By measuring the apparent shear viscosity in terms of Couette flow, we achieve a viscosity inhomogeneous system which may be applicable to nano particle processing. In the other example, we introduce a homeotropic spherical particle to the channel, and focus on the deformations of the defect ring due to anchorings and flow. The results are then compared to the molecular dynamics simulations of a colloid particle in an LC modeled by a Gay-Berne potential.
Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun
2012-01-01
We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2015-03-01
A lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) with divergence-free velocity field is proposed, and the Chapman-Enskog analysis shows that the CDE can be recovered correctly. In the present model, the convection term is treated as a source term in the lattice Boltzmann equation (LBE) rather than being directly recovered by LBE; thus the CDE is intrinsically solved as a pure diffusion equation with a corresponding source term. To avoid the adoption of a nonlocal finite-difference scheme for computing the convection term, a local scheme is developed based on the Chapman-Enskog analysis. Most importantly, by properly specifying the discrete source term in the moment space, the local scheme can reach the same order (ɛ2) at which the CDE is recovered by a LB model. Numerical tests, including a one-dimensional periodic problem, diffusion of a Gaussian hill, diffusion of a rectangular pulse, and natural convection in a square cavity, are carried out to verify the present model. Numerical results are satisfactorily consistent with analytical solutions or previous numerical results, and show higher accuracy due to the correct recovery of CDE.
An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions
Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe
2014-10-06
Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan and Chen (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence to isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented. Multi-range interactions have been used for SC model, but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong and Cheng. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.
Yamabe, Hirotatsu; Tsuji, Takeshi; Liang, Yunfeng; Matsuoka, Toshifumi
2015-01-01
CO2 geosequestration in deep aquifers requires the displacement of water (wetting phase) from the porous media by supercritical CO2 (nonwetting phase). However, the interfacial instabilities, such as viscous and capillary fingerings, develop during the drainage displacement. Moreover, the burstlike Haines jump often occurs under conditions of low capillary number. To study these interfacial instabilities, we performed lattice Boltzmann simulations of CO2-water drainage displacement in a 3D synthetic granular rock model at a fixed viscosity ratio and at various capillary numbers. The capillary numbers are varied by changing injection pressure, which induces changes in flow velocity. It was observed that the viscous fingering was dominant at high injection pressures, whereas the crossover of viscous and capillary fingerings was observed, accompanied by Haines jumps, at low injection pressures. The Haines jumps flowing forward caused a significant drop of CO2 saturation, whereas Haines jumps flowing backward caused an increase of CO2 saturation (per injection depth). We demonstrated that the pore-scale Haines jumps remarkably influenced the flow path and therefore equilibrium CO2 saturation in crossover domain, which is in turn related to the storage efficiency in the field-scale geosequestration. The results can improve our understandings of the storage efficiency by the effects of pore-scale displacement phenomena. PMID:25427299
Kim, Yong Hyun; Xu, Xiaofeng; Lee, Joon Sang
2010-07-01
The analysis of a flow pattern in cerebral aneurysms and the effect of stent strut shapes are presented in this article. The treatment of cerebral aneurisms with a porous stent has recently been proposed as a minimally invasive way to prevent rupture and favor coagulation mechanism inside the aneurism. The efficiency of stent is related to several parameters, including porosity and stent strut shapes. The goal of this article is to study the effect of the stent strut shape and porosity on the hemodynamic properties of the flow inside an aneurysm using a numerical analysis. In this study, we use the concept of flow reduction to characterize the stent efficiency. Also, we use the lattice Boltzmann method (LBM) of a non-Newtonian blood flow. To resolve the characteristics of a highly complex flow, we use an extrapolation method for the wall and stent boundary. To ease the code development and facilitate the incorporation of new physics, a scientific programming strategy based on object-oriented concepts is developed. Reduced velocity, smaller average vorticity magnitude, smaller average shear rate, and increased viscosity are observed when the proposed stent shapes and porosities are used. The rectangular stent is observed to be optimal and to decrease the magnitude of the velocity by 89.25% in the 2D model and 53.92% in the 3D model in the aneurysm sac. Our results show the role of the porosity and stent strut shape and help us to understand the characteristics of stent strut design. PMID:20300847
NASA Astrophysics Data System (ADS)
Khajepor, Sorush; Wen, John; Chen, Baixin
2015-02-01
Pseudopotential lattice Boltzmann (LB) models have been recognized as efficient numerical tools to simulate complex fluid systems, including those at thermodynamic equilibrium states and with phase transitions. However, when the equation of state (EOS) of real fluids is implemented, the existing pseudopotential LB models suffer from thermodynamic inconsistency. This study presents a multipseudopotential interparticle interaction (MPI) scheme, which is fully consistent with thermodynamics and applicable to engineering applications. In this framework, multiple pseudopotentials are employed to represent dominant interaction potentials at different extents of the mean free path of particles. By simulating van der Waals and Carnahan-Starling fluids, it is demonstrated that the MPI scheme can correctly simulate the physical nature of two-phase systems on the lattice including the continuum predictions of liquid-vapor coexistence states and the sound speeds in liquid and vapor phases. It is also shown that the lattice interactions of the MPI scheme represent underlying molecular interactions as they vary in a broad range from strong short-distance repulsions to weak long-distance attractions during phase transitions. Consequently, the MPI is proved to be a reliable LB scheme as it avoids generating unphysical potentials in implementing the EOSs of real fluids and limiting the spurious velocities at the interface of two-phase systems. Additionally, a straightforward procedure is suggested and discussed to preset the MPI system with the two-phase properties of a selected fluid.
Multiphase fluid simulations through porous rock using Shan-Chen type lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Qohar, Ulin Nuha Abdul; Latief, Fourier Dzar Eljabbar; Fauzi, Umar
2015-09-01
Fluid flow with multiphase components is one of the daily problems that interesting to learn and widely used in various fields, one of them in rock physics. Euler approach and Lagrange approach, the two models are applied to study the fluid flow, which often known as the microscopic and macroscopic approaches. Lattice Boltzmann Method combines the advantages and appropriate of both approaches, that is used as a more efficient model approach, also known as mesoscopic. The LB method has been used to model the two-phase fluid flow with different viscosities using the Shan-Chen model, this model explain the interaction between two different fluid phases. Validated numerical models compiled using two ways, namely analytical models and physical models. Based on this research, numerical models are designed to meet the analytical model with an error on the lattice at the edge of the lattice. When compared with physical models, numerical models have qualitatively suitability. Based on the results of the validation of numerical models, modeling is done to the image of porous rock which gives the results of multiphase fluid flow profile inside the pore. Moreover, the results obtained indicate that there are effective pores that fluid can not be drained.
Lattice Boltzmann Method for Liquid-Gas-Particle Systems with Compact Discretization
NASA Astrophysics Data System (ADS)
Lee, Taehun; Farokhirad, Samaneh
2015-11-01
We have developed a liquid-gas-particle (LGP) lattice Boltzmann method (LBM) that utilizes only the nearest neighbor lattice sites for the computation of intermolecular forcing terms. Previous LGP-LBM requires larger number of lattice sites to model the interaction of fluid interfaces with immersed solid particles. This makes the treatment of contact line on a particle cumbersome when the partially wetting particle interacts with liquid-gas interface. The new model is capable of suppressing spurious currents at equilibrium. Many existing multi-component solvers suffer from spurious currents and the inability to employ components with sufficiently large density differences due to stability issues. Due to their finite size and wetting properties, particles deform an interface locally, which can lead to capillary interactions that dramatically alter the behavior of the system, relative to the particle-free case. We will present the liquid-gas-particle algorithm and its validations, which include two-particles on a flat liquid-gas interface approaching each other due to capillary effects, and a particle-laden drop impact with various impaction velocities.
Simulations of Heated Bluff-Bodies with the Multi-Speed Entropic Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Frapolli, Nicolò; Chikatamarla, Shyam S.; Karlin, Ilya
2015-12-01
Two-dimensional simulations of heated circular and square cylinders are performed in order to validate a recently introduced entropic thermal lattice Boltzmann model (Frapolli et al. in Phys Rev E 90:043306, 2014), and the new boundary conditions for complex walls and multi-speed lattices. Validation is carried out by comparing simulation results with other reference simulations and experiments. For the hydrodynamic field, the wake structure was analyzed by means of the wake recirculation length for both steady and unsteady two-dimensional regimes, by comparing the Strouhal number of the vortex shedding associated with the first instability of the hydrodynamic field, and qualitatively by showing the streamlines for different Reynolds numbers. For the thermal part of the simulations, isotherms and mean Nusselt number are qualitatively and quantitatively compared with the literature results. All the computed quantities are found to agree excellently with the reference data available in the literature. This opens door for accurate simulations in complex geometries in thermal and compressible flow regimes with multi-speed lattices.
High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers
NASA Astrophysics Data System (ADS)
Feuchter, C.; Schleifenbaum, W.
2016-07-01
We analyze a large number of high-order discrete velocity models for solving the Boltzmann-Bhatnagar-Gross-Krook equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level, we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.
Technology Transfer Automated Retrieval System (TEKTRAN)
In this presentation we simulate saturated flow through macroporous soil columns (7.62x18 cm) with a lattice Boltzmann model and compare results with measured saturated hydraulic conductivities. Porous geometry was obtained with an industrial CT scanner yielding a resolution of 119 microns (656x656x...
On the application of the lattice Boltzmann method to the investigation of glottal flow
Kucinschi, Bogdan R.; Afjeh, Abdollah A.; Scherer, Ronald C.
2008-01-01
The production of voice is directly related to the vibration of the vocal folds, which is generated by the interaction between the glottal flow and the tissue of the vocal folds. In the current study, the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations. The numerical investigation is based on the lattice Boltzmann method (LBM), which is an alternative approach within computational fluid dynamics. Compared to the traditional Navier–Stokes computational fluid dynamics methods, the LBM is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator. The multiple relaxation time model was used to improve the numerical stability. The results obtained with LBM were compared to the results provided by a traditional Navier–Stokes solver and experimental data. It was shown that LBM results are satisfactory for all the investigated cases. PMID:18646995
Najafi-Yazdi, A; Mongeau, L
2012-09-15
The Lattice Boltzmann Method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier-Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems are presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor. PMID:23526050
Najafi-Yazdi, A.; Mongeau, L.
2012-01-01
The Lattice Boltzmann Method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier-Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems are presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor. PMID:23526050
Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations.
Papenkort, S; Voigtmann, Th
2014-04-28
We discuss pressure-driven channel flow for a model of shear-thinning glass-forming fluids, employing a modified lattice-Boltzmann (LB) simulation scheme. The model is motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions and captures a nonvanishing dynamical yield stress and the appearance of normal-stress differences and a flow-induced pressure contribution. The standard LB algorithm is extended to deal with tensorial, nonlinear constitutive equations of this class. The new LB scheme is tested in 2D pressure-driven channel flow and reproduces the analytical steady-state solution. The transient dynamics after startup and removal of the pressure gradient reproduce a finite stopping time for the cessation flow of yield-stress fluids in agreement with previous analytical estimates. PMID:24784287
Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods
NASA Astrophysics Data System (ADS)
Klassen, Alexander; Scharowsky, Thorsten; Körner, Carolin
2014-07-01
Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti-6Al-4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects.
Simulation of Ferrofluid Flow for Magnetic Drug Targeting Using the Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Kandelousi, Mohsen Sheikholeslami; Ellahi, Rahmat
2015-02-01
Influence of a spatially varying magnetic field on Fe3O4-plasma nanofluid flow in a vessel as a targeted drug delivery system is investigated. Combined effects of ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) are considered in mathematic models. The lattice Boltzmann method is applied to solve the governing equations. Effects of active parameters, such as the Reynolds number and magnetic number on the flow characteristics, have been examined. Results indicate that the presence of the magnetic field affects considerably the flow field. Back flow occurs near the region where the magnetic source is located. Also, it can be found that the skin friction coefficient is a decreasing function of the Reynolds number and magnetic number.
Grayscale lattice Boltzmann model for multiphase heterogeneous flow through porous media
NASA Astrophysics Data System (ADS)
Pereira, Gerald G.
2016-06-01
The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations.
Grayscale lattice Boltzmann model for multiphase heterogeneous flow through porous media.
Pereira, Gerald G
2016-06-01
The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations. PMID:27415381
NASA Astrophysics Data System (ADS)
Yu, H.; Wang, Z.; Zhang, C.; Chen, N.; Zhao, Y.; Sawchuk, A. P.; Dalsing, M. C.; Teague, S. D.; Cheng, Y.
2014-11-01
Existing research of patient-specific computational hemodynamics (PSCH) heavily relies on software for anatomical extraction of blood arteries. Data reconstruction and mesh generation have to be done using existing commercial software due to the gap between medical image processing and CFD, which increases computation burden and introduces inaccuracy during data transformation thus limits the medical applications of PSCH. We use lattice Boltzmann method (LBM) to solve the level-set equation over an Eulerian distance field and implicitly and dynamically segment the artery surfaces from radiological CT/MRI imaging data. The segments seamlessly feed to the LBM based CFD computation of PSCH thus explicit mesh construction and extra data management are avoided. The LBM is ideally suited for GPU (graphic processing unit)-based parallel computing. The parallel acceleration over GPU achieves excellent performance in PSCH computation. An application study will be presented which segments an aortic artery from a chest CT dataset and models PSCH of the segmented artery.
Imbalance-correction grid-refinement method for lattice Boltzmann flow simulations
NASA Astrophysics Data System (ADS)
Kuwata, Y.; Suga, K.
2016-04-01
To enhance the accuracy and applicability of the zonal grid refinement method for the lattice Boltzmann method, a new method which minimizes the interface imbalances of mass and momentum is developed. This method introduces a correction step for the macroscopic flow variables such as the fluid density and velocity to remove their interface discontinuity. To demonstrate and evaluate the presently developed imbalance correction grid refinement method, large eddy simulations of turbulent channel and square cylinder flows are carried out. By changing the grid arrangement in the turbulent channel flows, it is confirmed that the present method reduces the sensitivity to the location of the grid refinement interface and minimizes the unphysically discontinuous profiles satisfactorily. Furthermore, the present method considerably improves mass conservation of the system, which is particularly important for long time periodical flow simulations. It is also confirmed that the present method generally improves the prediction performance of the square cylinder flows.
NASA Astrophysics Data System (ADS)
Huang, Juntao; Hu, Zexi; Yong, Wen-An
2016-04-01
In this paper, we present a kind of second-order curved boundary treatments for the lattice Boltzmann method solving two-dimensional convection-diffusion equations with general nonlinear Robin boundary conditions. The key idea is to derive approximate boundary values or normal derivatives on computational boundaries, with second-order accuracy, by using the prescribed boundary condition. Once the approximate information is known, the second-order bounce-back schemes can be perfectly adopted. Our boundary treatments are validated with a number of numerical examples. The results show the utility of our boundary treatments and very well support our theoretical predications on the second-order accuracy thereof. The idea is quite universal. It can be directly generalized to 3-dimensional problems, multiple-relaxation-time models, and the Navier-Stokes equations.
Numerical simulations of immiscible displacement in the cavities via lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Liang, Hong; Chai, Zhenhua; Shi, Baochang; Guo, Zhaoli; Li, Qiuxiang
2015-12-01
In this paper, the immiscible displacements in the different cavities are studied by the pseudo-potential lattice Boltzmann (LB) model. We first validate the model with a two-dimensional (2D) layered flow, and find that the numerical results agree well with the corresponding analytical solutions. Then, we perform some numerical simulations to study the immiscible displacements in the cavities, and focus on the effects of the surface wettability, capillary number and density ratio on the displacement efficiency. The numerical results show that the displacement efficiency increases with the increase of the capillary number at first and then presents a decrease with the capillary number when it is large enough. The increase of the contact angle θ1 or decrease of the density ratio increases the displacement efficiency but decreases the critical capillary number. Finally, it is also found that both the size and geometry of cavity have a significant influence on the displacement efficiency.
Analysis of improved Lattice Boltzmann phase field method for soluble surfactants
NASA Astrophysics Data System (ADS)
van der Sman, R. G. M.; Meinders, M. B. J.
2016-02-01
In this paper we present a novel Lattice Boltzmann model for immiscible fluids with soluble surfactants adsorbing at the interface with improved numerical and extended physical properties. The numerical improvements are based on the use of an analytical representation of a regularized delta-function in the surface free energy functional for the surfactant. Furthermore, the physics of the system have been extended to differential solubility of the surfactant combined with the use of Frumkin sorption behaviour. This enables the scheme to approach more realistic systems like foams and emulsions. This novel scheme is much superior in numerical stability than our previous scheme, based on a squared gradient approximation. Furthermore, we have observed the phenomenon of interface broadening under certain conditions. This phenomenon limits the surface pressure to about 30% of the capillary pressure of a bare droplet. It remains to be investigated whether this interface broadening reflects some physical effect, as has been observed for proteins.
Modeling Particle-Laden Compressible Flows Using Lattice-Boltzmann Simulation
NASA Astrophysics Data System (ADS)
Ayala, Orlando; Thomas, John; Wang, Lian-Ping
2012-11-01
Combing the three-dimensional compressible Lattice-Boltzmann model with a fluid-particle interaction model, a robust computational framework for predicting fluid/solid momentum transfer within a particle-laden compressible flow field is developed. This tool is used to examine the effects of a moving shock front on the time-evolution of the displacement, velocity, and acceleration vectors of a single spherical particle initially at rest. These results are compared to analytical solutions obtained from the Navier-Stokes equations for compressible flows and a relationship between Mach number and drag coefficient is developed. Next, momentum transport through a system of particles is examined and the effects of particle-particle interactions on shock front propagation/attenuation are discussed. These results are used to understand fluid/solid momentum transfer within detonation shock waves.
Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.
Coon, Ethan; Porter, Mark L.; Kang, Qinjun; Moulton, John D.; Lichtner, Peter C.
2012-06-18
In spatially and temporally localized instances, capturing sub-reservoir scale information is necessary. Capturing sub-reservoir scale information everywhere is neither necessary, nor computationally possible. The lattice Boltzmann Method for solving pore-scale systems. At the pore-scale, LBM provides an extremely scalable, efficient way of solving Navier-Stokes equations on complex geometries. Coupling pore-scale and continuum scale systems via domain decomposition. By leveraging the interpolations implied by pore-scale and continuum scale discretizations, overlapping Schwartz domain decomposition is used to ensure continuity of pressure and flux. This approach is demonstrated on a fractured medium, in which Navier-Stokes equations are solved within the fracture while Darcy's equation is solved away from the fracture Coupling reactive transport to pore-scale flow simulators allows hybrid approaches to be extended to solve multi-scale reactive transport.
NASA Astrophysics Data System (ADS)
Pepona, Marianna; Favier, Julien
2016-09-01
In this work, we propose a numerical framework to simulate fluid flows in interaction with moving porous media of complex geometry. It is based on the Lattice Boltzmann method including porous effects via a Brinkman-Forchheimer-Darcy force model coupled to the Immersed Boundary method to handle complex geometries and moving structures. The coupling algorithm is described in detail and it is validated on well-established literature test cases for both stationary and moving porous configurations. The proposed method is easy to implement and efficient in terms of CPU cost and memory management compared to alternative methods which can be used to deal with moving immersed porous media, e.g. re-meshing at each time step or use of a moving/chimera mesh. An overall good agreement was obtained with reference results, opening the way to the numerical simulation of moving porous media for flow control applications.
Electrodeposition Modeling Using Coupled Phase-Field and Lattice Boltzmann Approach
NASA Astrophysics Data System (ADS)
Patil, D. V.; Premnath, K. N.; Desai, D.; Banerjee, Sanjoy
2014-01-01
In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg-Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO4 solution.
Lattice Boltzmann method for the age concentration equation in shallow water
NASA Astrophysics Data System (ADS)
Liu, Haifei; Ding, Yu; Wang, Hongda; Zhang, Jie
2015-10-01
Water age is a critical parameter in reflecting the extent of water exchange. It represents the time that water parcels or contaminants are transported from source to current positions. In this study, an equilibrium distribution function for water age concentration is proposed within the Eulerian framework based on the existing theory of water age, and it can recover the age concentration equation. In addition, the lattice Boltzmann method for water age in the Lagrangian procedures is developed. This method also enables the Lagrangian age to be fundamentally simulated under computationally expensive conditions. In numerical tests, cubic and circular reservoirs with narrow inflow-outflow boundaries are used to verify the applicability of the model. Finally, the proposed approaches are applied to the Baiyangdian Lake, the biggest freshwater lake in northern China. The result is compared with that acquired by the Environmental Fluid Dynamic Code (EFDC) as well.
NASA Astrophysics Data System (ADS)
Guzman, Orlando; Velez, Jose Antonio; Castañeda, David
2008-03-01
Experimental biosensors based on liquid crystals (LC) use nematics to detect the presence of specific analytes, via the optical textures exhibited by the LC at long times. Efforts to model the time evolution of these textures have relied on relaxational models, ignoring transport phenomena. In this work we include hydrodynamics into a model for these LC biosensors, using lattice Boltzmann (LB) methods and assess the effect on the lifetime of multidomain structures, characteristic of high concentrations of analyte. We apply Yeoman's et al. LB algorithm, which reproduces the hydrodynamic equations developed by Beris and Edwards for LCs. We also take into account thermal fluctuations, by adding random perturbations to the hydrodynamic modes. Following Adhikari et al., their amplitude is determined by the Fluctuation-Dissipation theorem and we excite both hydrodynamic and the sub-hydrodynamic modes (also called ghost modes). As a result, we analyze the influence of the fluctuations and hydrodynamics on the movement of topological defects.
NASA Astrophysics Data System (ADS)
Hilpert, M.; Long, W.
2006-05-01
We present a Lattice-Boltzmann model for bacterial chemotaxis that accounts, at the pore scale, for advective-diffusive transport of the bacteria and a reaction of the bacteria with a chemoattractant. The model was validated by simulating experiments on the degradation of naphthalene by Pseudomonas putida in a capillary tube containing either bulk liquid or glass beads. Naphthalene was initially uniformly distributed in the void space of a tube. Then, one tube inlet was brought into contact with a bacterial reservoir. We found that the biodegradation process involved the formation of a bacterial band propagating with constant speed into the tube while metabolizing the contaminant. In another set of simulations, we showed that bacterial chemotaxis may significantly effect and improve the biodegradation of a contaminant in flowing groundwater. Two bacterial bands may form if the chemoattractant is initially uniformly distributed: one band traveling upstream (towards a potential contamination source) and the other one downstream.
NASA Astrophysics Data System (ADS)
Kang, XiuYing
2015-01-01
By using the lattice Boltzmann method (LBM) pulsatile blood flows were simulated in three-dimensional moderate stenosed and recanalized carotid bifurcations to understand local hemodynamics and its relevance in arterial atherosclerosis formation and progression. The helical flow patterns, secondary flow and wall dynamical pressure spatiotemporal distributions were investigated, which leads to the disturbed shear forces in the carotid artery bifurcations. The wall shear stress distributions indicated by time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and the relative residence time (RRT) in a cardiac cycle revealed the regions where atherosclerotic plaques are prone to form, extend or rupture. This study also illustrates the point that locally disturbed flow may be considered as an indicator for early atherosclerosis diagnosis. Additionally the present work demonstrates the robust and highly efficient advantages of the LBM for the hemodynamics study of the human blood vessel system.
Grad's approximation for moving and stationary walls in entropic lattice Boltzmann simulations
NASA Astrophysics Data System (ADS)
Dorschner, B.; Chikatamarla, S. S.; Bösch, F.; Karlin, I. V.
2015-08-01
We introduce a new generalized wall boundary condition for the entropic lattice Boltzmann method (ELBM) that is capable of handling complex flow geometries including moving walls. The Grad's ten moments approximation is employed to approximate the missing populations at the boundary nodes. The new boundary condition significantly improves accuracy, stability and sub-grid features of LBM and in particular of its entropic variant, ELBM. The proposed boundary condition is tested for a range of flows in two dimensions, including planar channel flow, Couette flow, flow past a circular cylinder and sedimenting circular particles. Further simulations involving complex geometries such as flapping wing and transversely oscillating cylinder demonstrate superior stability and accuracy of the new wall boundary condition.
Development of a Prototype Lattice Boltzmann Code for CFD of Fusion Systems.
Pattison, Martin J; Premnath, Kannan N; Banerjee, Sanjoy; Dwivedi, Vinay
2007-02-26
Designs of proposed fusion reactors, such as the ITER project, typically involve the use of liquid metals as coolants in components such as heat exchangers, which are generally subjected to strong magnetic fields. These fields induce electric currents in the fluids, resulting in magnetohydrodynamic (MHD) forces which have important effects on the flow. The objective of this SBIR project was to develop computational techniques based on recently developed lattice Boltzmann techniques for the simulation of these MHD flows and implement them in a computational fluid dynamics (CFD) code for the study of fluid flow systems encountered in fusion engineering. The code developed during this project, solves the lattice Boltzmann equation, which is a kinetic equation whose behaviour represents fluid motion. This is in contrast to most CFD codes which are based on finite difference/finite volume based solvers. The lattice Boltzmann method (LBM) is a relatively new approach which has a number of advantages compared with more conventional methods such as the SIMPLE or projection method algorithms that involve direct solution of the Navier-Stokes equations. These are that the LBM is very well suited to parallel processing, with almost linear scaling even for very large numbers of processors. Unlike other methods, the LBM does not require solution of a Poisson pressure equation leading to a relatively fast execution time. A particularly attractive property of the LBM is that it can handle flows in complex geometries very easily. It can use simple rectangular grids throughout the computational domain -- generation of a body-fitted grid is not required. A recent advance in the LBM is the introduction of the multiple relaxation time (MRT) model; the implementation of this model greatly enhanced the numerical stability when used in lieu of the single relaxation time model, with only a small increase in computer time. Parallel processing was implemented using MPI and demonstrated the
A modified multiple-relaxation-time lattice Boltzmann model for convection-diffusion equation
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2014-10-01
A modified lattice Boltzmann model with multiple relaxation times (MRT) for the convection-diffusion equation (CDE) is proposed. By modifying the relaxation matrix, as well as choosing the corresponding equilibrium distribution function properly, the present model can recover the CDE with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the Chapman-Enskog analysis. This model is firstly validated by simulating the diffusion of a Gaussian hill, which demonstrates it can handle the anisotropic diffusion problem correctly. Then it is adopted to calculate the longitudinal dispersion coefficient of the Taylo-Aris dispersion. Numerical results show that the present model can further reduce the numerical error under the condition of non-zero velocity vector, especially when the dimensionless relaxation time is relatively large.
A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2014-02-01
In this paper, a new lattice Boltzmann model for the coupled nonlinear system of viscous Burgers’ equation is proposed by using the double evolutionary equations. Through selecting equilibrium distribution functions and amending functions properly, the governing evolution system can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. The effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail. The numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies. It is found that the numerical results agree well with the analytic solutions, which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous Burgers’ equation.
Lattice Boltzmann Simulation of Blood Flow in Blood Vessels with the Rolling Massage
NASA Astrophysics Data System (ADS)
Yi, Hou-Hui; Xu, Shi-Xiong; Qian, Yue-Hong; Fang, Hai-Ping
2005-12-01
The rolling massage manipulation is a classic Chinese massage, which is expected to improve the circulation by pushing, pulling and kneading of the muscle. A model for the rolling massage manipulation is proposed and the lattice Boltzmann method is applied to study the blood flow in the blood vessels. The simulation results show that the blood flux is considerably modified by the rolling massage and the explicit value depends on the rolling frequency, the rolling depth, and the diameter of the vessel. The smaller the diameter of the blood vessel, the larger the enhancement of the blood flux by the rolling massage. The model, together with the simulation results, is expected to be helpful to understand the mechanism and further development of rolling massage techniques.
On the search of more stable second-order lattice-Boltzmann schemes in confined flows
NASA Astrophysics Data System (ADS)
Golbert, D. R.; Blanco, P. J.; Clausse, A.; Feijóo, R. A.
2015-08-01
The von Neumann linear analysis, restricted by a heuristic selection of wave-number vectors was applied to the search of explicit lattice Boltzmann schemes which exhibit more stability than existing methods. The relative stability of the family members of quasi-incompressible collision kernels, for the Navier-Stokes equations in confined flows, was analyzed. The linear stability analysis was simplified by assuming a uniform velocity level over the whole domain, where only the wave numbers of the first harmonic normal to the flow direction were permitted. A singular equilibrium function that maximizes the critical velocity level was identified, which was afterwards tested in particular cases of confined flows of interest, validating the resulting procedure.
NASA Astrophysics Data System (ADS)
Gupta, Anupam
2015-11-01
The effects of viscoelasticity on the dynamics and break-up of liquid threads in microfluidic devices, i.e., T-junctions & Cross-Junction, are investigated using numerical simulations of dilute polymeric solutions for a wide range of Capillary numbers (Ca), i.e., changing the balance between the viscous forces and the surface tension at the interface. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time and the finite extensibility parameter, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. European Research Council under the Europeans Community's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement N. 297004.
Lattice Boltzmann simulation of multicomponent noncontinuum diffusion in fractal porous structures
NASA Astrophysics Data System (ADS)
Ma, Qiang; Chen, Zhenqian
2015-07-01
A lattice Boltzmann method (LBM) of multicomponent diffusion is developed to examine multicomponent, noncontinuum mass diffusion in porous media. An additional collision interaction is proposed to mimic the Knudsen diffusion caused by the collision interaction between gas molecules and solid pore walls. Using the improved LBM model, the ternary mixtures diffusion is simulated in fractal porous structures which are reconstructed by the random midpoint displacement algorithm. The effects of fractal characteristics and Knudsen diffusion resistance on the multicomponent diffusion in porous structures are investigated and discussed. The results indicate that the smaller fractal dimension enhances the diffusion rate of gas mixtures in fractal porous structures. When the dimensionless Knudsen diffusion coefficient is less than 20, the presence of Knudsen diffusion resistance reduces the rate of mass diffusion in porous structures obviously, especially for the species with larger molecular weight.
Simulation of Droplets Collisions Using Two-Phase Entropic Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Mazloomi Moqaddam, A.; Chikatamarla, S. S.; Karlin, I. V.
2015-12-01
The recently introduced entropic lattice Boltzmann model for multiphase flows (Mazloomi et al. in Phys Rev Lett 114:174502, 2015) is used to simulate binary droplet collisions. The entropy-based stabilization, together with a new polynomial equation of state, enhances performance of the model and allow us to simulate droplet collision for various Weber and Reynolds numbers and large liquid to vapor density ratio. Different types of droplet collision outcomes, namely coalescence, stretching separation and reflexive separation are recovered in a range of impact parameter for two equal sized droplets. The results demonstrated the essential role played by the surface tension, kinematic viscosity, impact parameter and relative velocity in the droplet collision dynamics leading to coalescence or separation collision outcomes. Comparison between numerical results and experiments in both coalescence and separation collisions demonstrate viability of the presented model.
NASA Astrophysics Data System (ADS)
Yu, Huidan; Zhang, Jinsuo; Li, Ning
2006-03-01
We investigate the enhancement of mass transfer in 2D thermally driven cavities using lattice Boltzmann equation (LBE) method. The computational technique integrates three coupled LBEs for solving velocity, temperature, and concentration fields simultaneously. Simulation is performed for oxygen transfer in lead/lead-bismuth eutectic with variations of temperature boundary, Schmidt number, and field aspect ratio to investigate the effects on enhancement of oxygen transfer. Interested characteristics include oxygen concentration, Sherwood number, and velocity profiles, etc. Our results clearly indicate that oxygen transfer is dominated by convection while diffusion also plays a role on it. Comparative studies demonstrate that side heating and top cooling device is more efficient to transfer oxygen than side heating and cooling device and oxygen transfers more rapidly in square cavity than in rectangular cavity. This work establishes a reliable thermal LBE model for thermally driven heat and mass transfer.
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
Fu, S.C.; So, R.M.C.; Leung, W.W.F.
2010-08-20
With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.
Lallemand; Luo
2000-06-01
The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyperviscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters that optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some two-dimensional LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long-wavelength limit (wave vector k=0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis. PMID:11088335
Lattice Boltzmann method simulations of Stokes number effects on particle motion in a channel flow
NASA Astrophysics Data System (ADS)
Zhang, Lenan; Jebakumar, Anand Samuel; Abraham, John
2016-06-01
In a recent experimental study by Lau and Nathan ["Influence of Stokes number on the velocity and concentration distributions in particle-laden jets," J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (<1) move toward the walls. Jebakumar et al. ["Lattice Boltzmann method simulations of Stokes number effects on particle trajectories in a wall-bounded flow," Comput. Fluids 124, 208 (2016)] have carried out simulations of a particle in a laminar channel flow to investigate this behavior. In their work, they report a similar behavior where particles with low St migrate toward the wall and oscillate about a mean position near the wall while those with high St oscillate about the channel center plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.
Lattice Boltzmann simulation of coalescence of multiple droplets on nonideal surfaces.
Zhou, Wenchao
2015-11-01
The interaction dynamics of droplets on a solid surface is a fundamental problem that is important to a wide variety of industrial applications, such as inkjet printing. Most previous research has focused on a single droplet and little research has been reported on the dynamics of multiple-droplet interactions on surfaces. Recently, Zhou et al. [W. Zhou, D. Loney, A. G. Fedorov, F. L. Degertekin, and D. W. Rosen, Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E 89, 033311 (2014)] reported an efficient numerical solver based on the lattice Boltzmann method (LBM) that enabled the simulation of the multiple-droplet interaction dynamics on an ideal surface (i.e., smooth and homogeneous). In order to predict the interaction dynamics in the real world, it is necessary to take into consideration the contact angle hysteresis phenomenon on a nonideal surface, which is possibly caused by the surface roughness and chemical inhomogeneity of the surface. In this paper a dynamic contact angle boundary condition is developed to take into account the contact angle hysteresis effect based on the previously reported LBM. The improved LBM is validated with experimental data from the literature. The influence of the droplet impact conditions (e.g., fluid properties and impingement velocity), droplet spacing, and surface conditions on the two-droplet interaction dynamics is investigated with the validated LBM. Interesting phenomena are observed and discussed. The interaction of a line of six droplets on a nonideal surface is simulated to demonstrate the powerful capability of the developed numerical solver in simulating the multiple-droplet interaction dynamics in the real world. PMID:26651816
Lattice Boltzmann Inverse Modeling of a Tracer Release in an Everglades Mangrove Estuary
NASA Astrophysics Data System (ADS)
Sukop, M. C.; Pearson, A. J.; Engel, V.; Ho, D. T.; Ferron Smith, S.
2011-12-01
The tidally-dominated Shark River is a major drainage of south Florida. The river passes through and nourishes North America's largest mangrove forest. Strong tidal flows in the river extend more than 12 km upstream from the river's mouth at the Gulf of Mexico. In November 2010, a deliberate release of SF6 tracer into the river was followed for several days to study the river's transport characteristics. During the tracer release and monitoring, tides led to a stage variation of about 0.8 m close to the Gulf and about 0.3 m in the river upstream of the tracer release point. The mangrove forest adjacent to the river is flooded at high tide and consists of mangrove roots and pneumatophores above highly porous peat root mass. Tracer movement and its analysis by conventional methods are complicated by these tidal flows and potentially by interaction with the mangrove zone groundwater. A 30-m resolution 2-dimensional Lattice Boltzmann model was constructed for a 30 x 21 km region of this part of southwestern Florida. Tidal stage boundaries were applied to the east and west edges of the domain. Based on aerial photography and a thresholding process, the domain was separated into open channels representing the complex river network and a porous medium representing the mangrove forest. SF6 concentrations were not monitored in these flood waters or groundwater during this experiment. The objective is to match the simulations to the SF6 observations in order to better understand chemical transport in this environment and to permit simulation of the transport of other species. Numerous conceptual and computational challenges have to be surmounted to apply Lattice Boltzmann methods to this problem.
NASA Technical Reports Server (NTRS)
Lallemand, Pierre; Luo, Li-Shi
2000-01-01
The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.
Lattice Boltzmann simulation of coalescence of multiple droplets on nonideal surfaces
NASA Astrophysics Data System (ADS)
Zhou, Wenchao
2015-11-01
The interaction dynamics of droplets on a solid surface is a fundamental problem that is important to a wide variety of industrial applications, such as inkjet printing. Most previous research has focused on a single droplet and little research has been reported on the dynamics of multiple-droplet interactions on surfaces. Recently, Zhou et al. [W. Zhou, D. Loney, A. G. Fedorov, F. L. Degertekin, and D. W. Rosen, Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E 89, 033311 (2014), 10.1103/PhysRevE.89.033311] reported an efficient numerical solver based on the lattice Boltzmann method (LBM) that enabled the simulation of the multiple-droplet interaction dynamics on an ideal surface (i.e., smooth and homogeneous). In order to predict the interaction dynamics in the real world, it is necessary to take into consideration the contact angle hysteresis phenomenon on a nonideal surface, which is possibly caused by the surface roughness and chemical inhomogeneity of the surface. In this paper a dynamic contact angle boundary condition is developed to take into account the contact angle hysteresis effect based on the previously reported LBM. The improved LBM is validated with experimental data from the literature. The influence of the droplet impact conditions (e.g., fluid properties and impingement velocity), droplet spacing, and surface conditions on the two-droplet interaction dynamics is investigated with the validated LBM. Interesting phenomena are observed and discussed. The interaction of a line of six droplets on a nonideal surface is simulated to demonstrate the powerful capability of the developed numerical solver in simulating the multiple-droplet interaction dynamics in the real world.
NASA Astrophysics Data System (ADS)
Saomoto, H.; Kase, Y.; Matsushima, T.; Yamada, Y.
2012-12-01
An accurate velocity model of porous flow plays an important role in the prediction of the ground water pollution.To clarify the behavior of porous flow passing through irregularly shaped grains, we have been performed CFD simulation and direct observation based on the Lattice Boltzmann Method and the LAT-PIV visuallization technique respectively. The Lattice Boltzmann simulator, which works on a graphics processing unit(GPU), is employed to evaluate the pore fluid velocity distribution in an accurate three dimensional digital model involving Toyoura sand. From the simulation results, the pore fluid velocity distributions converge into a unique non-gaussian distribution under various Reynolds numbers ranging from 2 to 10. The features of the non-gaussian distribution are summarized as follows: (1)It has a long tail until sextuple of the mean velocity magnitude. (2)It has a peak frequency close to zero velocity magnitude. (3)It slightly contains negative velocities. The LAT-PIV visuallization technique, a kind of laser slicing visualization method combined LAT(Laser-Aided Tomography) and PIV (Particle Image Velocimetry), visualizes both grain edges and pore fluid behavior inside specimen which is composed of crashed glass grains and specially blended silicone oil. The pore fluid velocity distributions captured by the LAT-PIV images indicate a similar tendency compared with those measured by the LBM simulations. This supports that the LBM simulation has sufficient ability to predict the pore fluid flow even if the porous medium is composed of irregularly shaped grains. GPU accelerated LBM simulation for Toyoura sand model Pore fluid velocity magnitude distributions for several Reynolds numbers
An immersed boundary-thermal lattice Boltzmann method for solid-liquid phase change
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2014-11-01
In this work, an immersed boundary-thermal lattice Boltzmann method (IB-TLBM) is proposed to simulate solid-liquid phase change problems. To treat the velocity and temperature boundary conditions on the solid-liquid interface, immersed boundary method (IBM) is adopted, in which the solid-liquid interface is represented as a sharp interface rather than a diffusive interface and is tracked explicitly by Lagrangian grid. The surface forces along the immersed boundary, including the “momentum force” for velocity boundary condition and the “energy force” for temperature boundary condition, are calculated by the direct-forcing scheme. The moving velocity of solid-liquid interface induced by phase change is calculated by the amount of latent heat absorbed or released in a time step directly, with no need to compute temperature gradients in solid and liquid phases separately. The temperature on the solid-liquid interface is specified as the melting temperature, which means phase change happens at a constant temperature. As the solid-liquid interface evolves with time, the identification of phase of Eulerian points and the rearrangement of Lagrangian points are also considered. With regard to the velocity and temperature fields, passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time (MRT) collision schemes is adopted. Numerical examples, including conduction-induced melting in a semi-infinite space and melting in a square cavity, are carried out to verify the present method and good results are obtained. As a further application, melting in a circular cylinder with considering the motion of solid phase is simulated successfully by the present method; numerical results show that the motion of solid phase accelerates the melting process obviously.
Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
Mohammadipoor, O R; Niazmand, H; Mirbozorgi, S A
2014-01-01
Since the lattice Boltzmann method originally carries out the simulations on the regular Cartesian lattices, curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved-boundary problems is extrapolating or interpolating macroscopic properties of boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation or interpolation in boundary conditions potentially causes abrupt changes in particle distributions. Therefore, a curved-boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to potential fields. The proposed treatment is tested against several well-established problems and the solutions order of accuracy is evaluated. Numerical results show that the present treatment is of second-order accuracy and has reliable stability characteristics. PMID:24580362
Lattice Boltzmann modeling of permeability in porous materials with partially percolating voxels.
Li, Ruru; Yang, Y Sam; Pan, Jinxiao; Pereira, Gerald G; Taylor, John A; Clennell, Ben; Zou, Caineng
2014-09-01
A partial-bounce-back lattice Boltzmann model has been used to simulate flow on a lattice consisting of cubic voxels with a locally varying effective percolating fraction. The effective percolating fraction of a voxel is the total response to the partial-bounce-back techniques for porous media flow due to subvoxel fine structures. The model has been verified against known analytic solutions on two- and three-dimensional regular geometries, and has been applied to simulate flow and permeabilities of two real-world rock samples. This enables quantitative determination of permeability for problems where voxels cannot be adequately segmented as discrete compositions. The voxel compositions are represented as volume fractions of various material phases and void. The numerical results have shown that, for the tight-sandstone sample, the bulk permeability is sensitive to the effective percolating fraction of calcite. That is, the subvoxel flow paths in the calcite phase are important for bulk permeability. On the other hand, flow in the calcite phase in the sandstone sample makes an insignificant contribution to the bulk permeability. The calculated permeability value for the sandstone sample is up to two orders of magnitude greater than the tight sandstone. This model is generic and could be applied to other oil and gas reservoir media or to material samples. PMID:25314558
NASA Astrophysics Data System (ADS)
Long, W.
2005-12-01
Responding to changes in the environment is a fundamental property of a living bacterium. Chemotaxis, the migration of microorganisms under the influence of a chemical gradient, navigates bacteria to an optimum environment. Chemotactic bacteria can either move towards a chemoattractant following a chemical gradient, or move away from a chemorepellent. Understanding chemotactic behavior is important for understanding biodegradation in groundwater systems. A numerical model based on a Lattice-Boltzmann method was developed to simulate chemotaxis in free liquids and porous media. This model accounts for bacterial chemotaxis and reactive transport of a chemoattractant. The microorganisms and chemoattractant are represented by quasi-particles that move, collide, and react with each other on a three-dimensional numerical lattice. The model was validated by simulating experiments on the degradation of naphthalene by Pseudomonas putida in a capillary tube containing either bulk liquid or glass beads. The agreement between the simulation results and the experimental data is excellent. From the simulations, we found that a fraction of bacteria detaches from the bacterial reservoir to form a traveling band, which enhances naphthalene removal in the capillary tube. In another set of simulations, we showed that bacterial chemotaxis may significantly effect and improve the biodegradation of a contaminant in flowing groundwater.
Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions
NASA Astrophysics Data System (ADS)
Hu, Zexi; Huang, Juntao; Yong, Wen-An
2016-04-01
In this work, we propose an interfacial scheme accompanying the lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, including conjugate conditions with or without jumps in heat and mass transfer, continuity of macroscopic variables and normal fluxes in ion diffusion in porous media with different porosity, and the Kapitza resistance in heat transfer. The construction of this scheme is based on our boundary schemes [Huang and Yong, J. Comput. Phys. 300, 70 (2015), 10.1016/j.jcp.2015.07.045] for Robin boundary conditions on straight or curved boundaries. It gives second-order accuracy for straight interfaces and first-order accuracy for curved ones. In addition, the new scheme inherits the advantage of the boundary schemes in which only the current lattice nodes are involved. Such an interfacial scheme is highly desirable for problems with complex geometries or in porous media. The interfacial scheme is numerically validated with several examples. The results show the utility of the constructed scheme and very well support our theoretical predications.
Pore-scale simulation of miscible displacement in porous media using the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Xia, Ming
2016-03-01
A numerical model based on the lattice Boltzmann method is presented to investigate the viscous fingering phenomena of miscible displacement processes in porous media, which involves the fluid flow, heat transfer and mass transport. Especially, temperature- and concentration-dependent pore-fluid viscosity is considered. A complete list is derived and given for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled problems involving fluid flow, heat transfer and mass transport using the LBM. To demonstrate the proposed model capacity, two different complex geometry microstructures using high resolution micro-computed tomography (micro-CT) images of core sample have been obtained and incorporated as computation geometries for modeling miscible displacement processes in porous media. The viscous fingering phenomena of miscible displacement processes are simulated in two different cases, namely in a channel and a porous medium respectively. Some influencing factors on the miscible displacement process, such as the pore-scale microstructure, Le number and Re number, are studied in great detail. The related simulation results have demonstrated that: (1) the existence of the pore-scale microstructure can have a significant effect on the front morphologies and front propagation speed in the miscible displacement process; (2) as the Le number increases, the fluid front and thermal front evolve differently, with the thermal front being less unstable due to more diffusion; (3) a larger Re number can lead to an increase in the propagation speed of the front.
A comparison of lattice-Boltzmann and Brownian dynamics simulations of dilute polymer solutions
NASA Astrophysics Data System (ADS)
Ladd, Tony; Kekre, Rahul; Butler, Jason
2008-11-01
We have compared lattice-Boltzmann and Brownian dynamics simulations of a single flexible polymer, in isolation and in confined geometries. In the case of the isolated chain we find agreement to within 1% in the diffusion coefficient and the Rouse mode relaxation times. We have obtained good agreement for the concentration profiles in a bounded shear flow, but the Brownian dynamics simulations currently use a superposition of the hydrodynamic fields generated by the walls. We expect to know the effects of the inter-wall correction by the time of the meeting. We have gone to some lengths to match the conditions of both simulations as closely as possible. We use identical potential parameters and correct for the differences between the periodic boundaries used in the LB simulations and the unbounded domains used in the BD simulations. We use very long runs, of the order of 10000 times the longest relaxation time, to reduce the statistical uncertainties to less than 0.1%. We find excellent agreement in the relaxation times over a wide range of temperatures and fluid viscosity. The most quantitative agreement is achieved in the weak coupling limit, where the hydrodynamic radius of the monomers is less than one quarter of the lattice spacing.
Chapman-Enskog analyses on gray lattice Boltzmann schemes for fluid flow in porous media
NASA Astrophysics Data System (ADS)
Chen, Chen; Li, Like; Mei, Renwei; Klausner, James
2014-11-01
Gray lattice Boltzmann (GLB) schemes have recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional reflection coefficient θ, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for linear drag of the medium. These schemes are very easy to implement; but there exists uncertainty about the need for redefining macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from various GLB schemes. In this work, Chapman-Enskog analyses are performed to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in ɛ only if θ = O(ɛ) in which ɛ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When gravitational force is considered or a body force is used to represent pressure gradient, the forcing term requires a modification factor that accounts for the effect of θ. The modification factor is derived for each combination of the forcing implementation method and the GLB scheme. The theoretical findings are verified by numerical results.
Conjugate heat and mass transfer in the lattice Boltzmann equation method
Li, LK; Chen, C; Mei, RW; Klausner, JF
2014-04-22
An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved
Strongly Correlated Quantum Gases Trapped in 3D Spin-Dependent Optical Lattices
NASA Astrophysics Data System (ADS)
Demarco, Brian
2011-03-01
Optical lattices have emerged as ideal systems for exploring Hubbard model physics, since the equivalent of material parameters such as the ratio of tunneling to interaction energy are easily and widely tunable. In this talk I will discuss our recent measurements using novel lattice potentials to realize more complex Hubbard models for bosonic 87 Rb atoms. In these experiments, we adjust the polarization of the lattice laser beams to realize fully three-dimensional, spin-dependent cubic optical lattices. We demonstrate that atoms can be trapped in combinations of spin states for which superfluid and Mott-insulator phases exist simultaneously in the lattice. We also co-trap states that experience a strong lattice potential and no lattice potential whatsoever. I will discuss recent measurements revealing a mechanism similar to Kapitza resistance that leads to thermal decoupling in this latter combination. The implications for sympathetic cooling and thermometry using species-dependent lattices will be outlined.
Lattice Boltzmann multi-phase simulations in porous media using Multiple GPUs
NASA Astrophysics Data System (ADS)
Toelke, J.; De Prisco, G.; Mu, Y.
2011-12-01
Ingrain's digital rock physics lab computes the physical properties and fluid flow characteristics of oil and gas reservoir rocks including shales, carbonates and sandstones. Ingrain uses advanced lattice Boltzmann methods (LBM) to simulate multiphase flow in the rocks (porous media). We present a very efficient implementation of these methods based on CUDA. Because LBM operates on a finite difference grid, is explicit in nature, and requires only next-neighbor interactions, it is suitable for implementation on GPUs. Since GPU hardware allows for very fine grain parallelism, every lattice site can be handled by a different core. Data has to be loaded from and stored to the device memory in such a way that dense access to the memory is ensured. This can be achieved by accessing the lattice nodes with respect to their contiguous memory locations [1,2]. The simulation engine uses a sparse data structure to represent the grid and advanced algorithms to handle the moving fluid-fluid interface. The simulations are accelerated on one GPU by one order of magnitude compared to a state of the art multicore desktop computer. The engine is parallelized using MPI and runs on multiple GPUs in the same node or across the Infiniband network. Simulations with up to 50 GPUs in parallel are presented. With this simulator using it is possible to perform pore scale multi-phase (oil-water-matrix) simulations in natural porous media in a commercial manner and to predict important rock properties like absolute permeability, relative permeabilites and capillary pressure [3,4]. Results and videos of these simulations in complex real world porous media and rocks are presented and discussed.
Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Januszewski, M.; Kostur, M.
2014-09-01
We present Sailfish, an open source fluid simulation package implementing the lattice Boltzmann method (LBM) on modern Graphics Processing Units (GPUs) using CUDA/OpenCL. We take a novel approach to GPU code implementation and use run-time code generation techniques and a high level programming language (Python) to achieve state of the art performance, while allowing easy experimentation with different LBM models and tuning for various types of hardware. We discuss the general design principles of the code, scaling to multiple GPUs in a distributed environment, as well as the GPU implementation and optimization of many different LBM models, both single component (BGK, MRT, ELBM) and multicomponent (Shan-Chen, free energy). The paper also presents results of performance benchmarks spanning the last three NVIDIA GPU generations (Tesla, Fermi, Kepler), which we hope will be useful for researchers working with this type of hardware and similar codes. Catalogue identifier: AETA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License, version 3 No. of lines in distributed program, including test data, etc.: 225864 No. of bytes in distributed program, including test data, etc.: 46861049 Distribution format: tar.gz Programming language: Python, CUDA C, OpenCL. Computer: Any with an OpenCL or CUDA-compliant GPU. Operating system: No limits (tested on Linux and Mac OS X). RAM: Hundreds of megabytes to tens of gigabytes for typical cases. Classification: 12, 6.5. External routines: PyCUDA/PyOpenCL, Numpy, Mako, ZeroMQ (for multi-GPU simulations), scipy, sympy Nature of problem: GPU-accelerated simulation of single- and multi-component fluid flows. Solution method: A wide range of relaxation models (LBGK, MRT, regularized LB, ELBM, Shan-Chen, free energy, free surface) and boundary conditions within the lattice
NASA Astrophysics Data System (ADS)
Muders, Dirk
1995-08-01
Exploring the clumpy and filamentary structure of interstellar molecular clouds is one of the key problems of modern astrophysics. So far, we have little knowledge of the physical processes that cause the structure, but turbulence is suspected to be essential. In this thesis I study turbulent flows and how they contribute to the structure of interstellar dark clouds. To this end, three-dimensional numerical hydrodynamic simulations are needed since the detailed turbulent spatial and velocity structure cannot be analytically calculated. I employ the ``Lattice Boltzmann Method'', a recently developed numerical method which solves the Boltzmann equation in a discretized phase space. Mesoscopic particle packets move with fixed velocities on a Cartesian lattice and at each time step they exchange mass according to given rules. Because of its mainly local operations the method is well suited for application on parallel or clustered computers. As part of my thesis I have developed a parallelized ``Lattice Boltzmann Method'' hydrodynamics code. I have improved the numerical stability for Reynolds numbers of up to 104.5 and Mach numbers of up to 0.9 and I have extended the method to include a second miscible fluid phase. The code has been used on the three currently most powerful workstations at the ``Max-Planck-Institut für Radioastronomie'' in Bonn and on the massively parallel mainframe CM-5 at the ``Gesellschaft für Mathematik und Datenverarbeitung'' in St. Augustin. The simulations consist of collimated shear flows and the motion of molecular clumps through an ambient medium. The dependence of the emerging structure on Reynolds and Mach numbers is studied. The main results are (1) that distinct clumps and filaments appear only at the transition between laminar and fully turbulent flow at Reynolds numbers between 500 and 5000 and (2) that subsonic viscous shear flows are capable of producing the dark cloud velocity structure. The unexpectedly low Reynolds numbers can
Predictions of nearshore hydrodynamics based on free-surface lattice Boltzmann approximations
NASA Astrophysics Data System (ADS)
Frandsen, J. B.; Mier-Torrecilla, M.; Zurita-Gotor, M.; Holman, D. M.
2012-04-01
The focus of the present free-surface model developments is to utilize gas dynamics theory to predict and investigate underlying mechanisms of the dynamics of nonlinear water waves. Since water wave mechanics is a topic not concerned with the notions from thermodynamics, the basics of the physics of incompressible gas dynamics provides a relatively simple means for describing the theory and predictions of nonlinear wave propagation through advanced random and nonlinear particle collision processes [1]. Nonlinear free-surface physics are investigated using the Lattice Boltzmann Method (LBM) at intermediate to shallow water depth. The LBM simulates fluid flow by tracking particle distributions in a Lagrangian manner. The particles are constrained to move on regular or octree lattices depending on wave steepness and/or wave-structure interaction details sought. The Boltzmann equation relates the time evolution and spatial variation of a collection of molecules to a collision operator that describes the interaction of the molecules. Mathematically, the collision integral of the LB equation poses difficulties when solution of the equation is sought. Investigators overcome this through descriptions of models with different levels of accuracy in the approximations of the integral. We consider a model in which the collision assumption is approximated by a multiple relaxation time form. The free-surface algorithm involves an interface tracking scheme based on the volume fraction of the fluid combined with the LBM for the advection equation in which the solver reconstructs the missing probability distribution functions taking into account the distance to the interface [2, 3]. The approximate forms of the LBM describe comparisons of the nonlinear shallow water equations and the Navier Stokes equations. Test cases involving predictions of run-up/run-down on cylinders and beaches are shown. The wet-dry interface conditions, viscosity treatment, surface break-up amongst others
Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models.
Huang, Haibo; Krafczyk, Manfred; Lu, Xiyun
2011-10-01
Numerous schemes have been proposed to incorporate a bulk forcing term into the lattice Boltzmann equation. In this paper we present a simple and straightforward comparative analysis of five popular schemes [Shan and Chen, Phys. Rev. E 47, 1815 (1993); Phys Rev Lett. 81, 1618 (1998); He et al., Phys. Rev. E 57, R13 (1998); Guo et al., Phys. Rev. E 65, 046308 (2002); Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)] in which their differences and similarities are identified. From the analysis we classify the schemes into two groups; the behaviors of the schemes in each group are proven to be identical up to second order. Numerical test simulating the two-dimensional unsteady Taylor-Green vortex flow problem demonstrate that all five schemes are of comparable accuracy for single-phase flow. However, for two-phase flow the situation is different, which is demonstrated by incorporating these schemes into different Shan-Chen-type multiphase models. The forcing scheme in the original Shan-Chen (SC) multiphase model turns out to be inaccurate in terms of the resulting surface tension for different density ratios and relaxation times. In the numerical tests, a typical equation of state and interparticle interactions including next-nearest neighbors were incorporated into the SC model. Our results confirm that the surface-tension values obtained from the original SC lattice Boltzmann method (LBM) simulation depend on the value of the relaxation time τ. For τ<0.7Δt, the surface tension agree well with the analytical solutions. However, when τ>0.7Δt, the surface tension turns out to be systematically larger than the analytical one, exceeding it by more than a factor of 2 for τ=2Δt. In contrast, with the application of the scheme proposed by He et al., the SC LBM produces very accurate surface tensions independent of the value of τ. We also found that the densities of the coexisting liquid and gas can be adjusted to match those at thermodynamic equilibrium if the
NASA Astrophysics Data System (ADS)
Schaap, M. G.; Tuller, M.; Guber, A.; Martin, M. A.; Martinez, F. S.; Pachepsky, Y.
2007-12-01
Soil structure greatly affects the ability of soil to transmit and to retain water, chemicals, and colloidal particles that can carry contaminants or be contaminants themselves, e.g. pathogenic microorganisms. No theory or empirical relationships have been developed to date to quantitatively relate parameters of soil structure and parameters of the contaminant transport in soils. The absence of theoretical advances in this area seriously hampers the ability to address issues of public concern, e.g. spread of contaminants introduced in the environment by agricultural activities. Recently, computer tomography of soils has become available to generate detailed images of soil pore space with high resolution and density. Successful applications of computer tomography in medical and material sciences show the great potential of this technique to create an exhaustive characterization of soil structure heterogeneity. In this presentation we investigate saturated flow through twelve undisturbed macroporous soil columns (7.62- cm sample diameter and 18-cm length) with lattice Boltzmann simulations. Saturated flow was measured for the complete columns, as well as on 2 cm sections for selected columns. Computed X-Ray tomography was performed on each of the columns, using the 420 kV X-ray source of a HYTEC FlashCT high-speed industrial CT scanner. The resolution was 116 microns per voxel, yielding a final tomography image of 656x656x1482 (~ 6.3 10E8) voxels. X-Ray CT observations typically provide "gray-scale" representations of the imaged object that must be segmented to yield discrete pore and particle geometry. Many segmentation algorithms are available, each yielding different final pore geometries thus potentially creating uncertainties in subsequent flow analyses. Lattice Boltzmann (LB) simulations will be presented only for some of the columns as the simulations are extremely computationally intensive (each simulation requires ~ 60 GB of computer RAM at the observed
Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth
NASA Astrophysics Data System (ADS)
Jelinek, Bohumir; Eshraghi, Mohsen; Felicelli, Sergio; Peters, John F.
2014-03-01
An extremely scalable lattice Boltzmann (LB)-cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Catalogue identifier: AEQZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29,767 No. of bytes in distributed program, including test data, etc.: 3131,367 Distribution format: tar.gz Programming language: Fortran 90. Computer: Linux PC and clusters. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI
Lattice Boltzmann Simulation of Multiphase Transport in Nanostructured PEM Fuel Cells
NASA Astrophysics Data System (ADS)
Stiles, Christopher D.
As the fossil fuel crisis becomes more critical, it is imperative to develop renewable sources of power generation. Polymer electrolyte membrane (PEM) fuel cells are considered a viable option. However, the cost of the platinum catalyst has hindered their commercialization. PEM fuel cells with platinum loading of >0.4 mg cm2 are common. Efforts towards further reducing this loading are currently underway utilizing nanostructured electrodes. A consequence of increased platinum utilization per unit area and thinner nanostructured electrodes is flooding, which is detrimental to fuel cell performance. Flooding causes a two-fold impact on cell performance: a drop in cell voltage and a rise in parasitic pumping power to overcome the increased pressure drop, which together result in a significant reduction in system efficiency. Proper water management is therefore crucial for optimum performance of the fuel cell and also for enhancing membrane durability. The goal of this thesis is to simulate the multiphase fluid transport in the nanostructured PEMFC of H2O in air with realistic density ratios. In order to pursue this goal, the ability of the pseudopotential based multiphase lattice Boltzmann method to realistically model the coexistence of the gas and liquid phases of H2O at low temperatures is explored. This method is expanded to include a gas mixture of O2 and N 2 into the multiphase H2O systems. Beginning with the examination of the phase transition region described by the current implementation of the multiphase pseudopotential lattice Boltzmann model. Following this, a modified form of the pressure term with the use of a scalar multiplier kappa for the Peng-Robinson equation of state is thoroughly investigated. This method proves to be very effective at enabling numerically stable simulations at low temperatures with large density ratios. It is found that for decreasing values of kappa, this model leads to an increase in multiphase interface thickness and a
NASA Astrophysics Data System (ADS)
Liu, Qing; He, Ya-Ling
2015-11-01
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid interface is traced through the liquid fraction which is determined by the enthalpy-based method. The present model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.
Shi, Xing; Lin, Guang; Zou, Jianfeng; Fedosov, Dmitry A.
2013-07-20
To model red blood cell (RBC) deformation in flow, the recently developed LBM-DLM/FD method ([Shi and Lim, 2007)29], derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain methodthe fictitious domain method, is extended to employ the mesoscopic network model for simulations of red blood cell deformation. The flow is simulated by the lattice Boltzmann method with an external force, while the network model is used for modeling red blood cell deformation and the fluid-RBC interaction is enforced by the Lagrange multiplier. To validate parameters of the RBC network model, sThe stretching numerical tests on both coarse and fine meshes are performed and compared with the corresponding experimental data to validate the parameters of the RBC network model. In addition, RBC deformation in pipe flow and in shear flow is simulated, revealing the capacity of the current method for modeling RBC deformation in various flows.
NASA Astrophysics Data System (ADS)
Xie, Hai-Qiong; Zeng, Zhong; Zhang, Liang-Qi; Liang, Gong-You; Hiroshi, Mizuseki; Yoshiyuki, Kawazoe
2012-12-01
In this paper, an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface, where the surface tension is implemented. The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid, an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface, and an indicator function is introduced to update the fluid properties accurately. The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points, and then the surface tension is directly computed by using the normal vector and curvature of the interface. Two benchmark problems, including Laplace's law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation. Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.
Numerical Analysis of Non-Darcy CH4 Flow in Fracture Network of Coal Using Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Zhang, Q.; Ju, Y.; Zheng, J.; Gong, W.
2015-12-01
Coal seams comprise fractured coal that is naturally separated by discontinuous fractures or joints. These discontinuous fractures constitute a complicated fracture network that leads to the Non-Darcy CH4 flow. It is intractable for conventional models to describe the behavior and its mechanism of Non-Darcy CH4 flow in fractured coal. This paper reports a promising numerical analysis of the complex CH4 flow in the fracture network of coal using Lattice Boltzmann Method (LBM). The flow properties of CH4 flow, including viscosity distribution, average flow speed, permeability coefficient, are derived using the LBM model. The analysis is validated by comparing the LBM results with the experimental observation data. Key words: Non-Darcy flow, CH4, fracture network, Lattice Boltzmann Method, Coal, Permeability
NASA Astrophysics Data System (ADS)
Jeon, Dong Hyup; Kim, Hansang
2015-10-01
The effect of the compression ratio on the dynamic behavior of liquid water transport in a gas diffusion layer (GDL) is studied both experimentally and numerically. We experimentally study the emergence and growth of liquid droplets in a channel at various compression ratios by adopting a direct visualization device. The results of the experiment show that water breakthrough occurs at the channel for a low compression ratio, whereas it is observed at the channel/rib interface for a high compression ratio. To determine the mechanism of water transport in the GDL, a multiphase lattice Boltzmann method (LBM) is developed for a simplified porous structure of the GDL. The observation of lattice Boltzmann (LB) simulation shows that the compression ratio significantly affects the water transport in the GDL. The results indicate that the lower compression ratio reduces the water saturation in the GDL. The simulation and experimental result are similar.
Physical and computational scaling issues in lattice Boltzmann simulations of binary fluid mixtures.
Cates, M E; Desplat, J-C; Stansell, P; Wagner, A J; Stratford, K; Adhikari, R; Pagonabarraga, I
2005-08-15
We describe some scaling issues that arise when using lattice Boltzmann (LB) methods to simulate binary fluid mixtures--both in the presence and absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) LB cannot fully resolve the hierarchy of length, energy and time-scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed; an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale-up simulations to very large lattice sizes? The problem is acute for systems undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimizing such effects are discussed. PMID:16099757
Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis
NASA Astrophysics Data System (ADS)
Ba, Yan; Liu, Haihu; Sun, Jinju; Zheng, Rongye
2013-10-01
Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis , IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/hxr008 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.
Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.
Liu, Haihu; Valocchi, Albert J; Kang, Qinjun
2012-04-01
We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35
Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations
NASA Astrophysics Data System (ADS)
Liu, Haihu; Valocchi, Albert J.; Kang, Qinjun
2012-04-01
We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35
NASA Astrophysics Data System (ADS)
Raabe, D.
2004-11-01
The article gives an overview of the lattice Boltzmann method as a powerful technique for the simulation of single and multi-phase flows in complex geometries. Owing to its excellent numerical stability and constitutive versatility it can play an essential role as a simulation tool for understanding advanced materials and processes. Unlike conventional Navier-Stokes solvers, lattice Boltzmann methods consider flows to be composed of a collection of pseudo-particles that are represented by a velocity distribution function. These fluid portions reside and interact on the nodes of a grid. System dynamics and complexity emerge by the repeated application of local rules for the motion, collision and redistribution of these coarse-grained droplets. The lattice Boltzmann method, therefore, is an ideal approach for mesoscale and scale-bridging simulations. It is capable to tackling particularly those problems which are ubiquitous characteristics of flows in the world of materials science and engineering, namely, flows under complicated geometrical boundary conditions, multi-scale flow phenomena, phase transformation in flows, complex solid-liquid interfaces, surface reactions in fluids, liquid-solid flows of colloidal suspensions and turbulence. Since the basic structure of the method is that of a synchronous automaton it is also an ideal platform for realizing combinations with related simulation techniques such as cellular automata or Potts models for crystal growth in a fluid or gas environment. This overview consists of two parts. The first one reviews the philosophy and the formal concepts behind the lattice Boltzmann approach and presents also related pseudo-particle approaches. The second one gives concrete examples in the area of computational materials science and process engineering, such as the prediction of lubrication dynamics in metal forming, dendritic crystal growth under the influence of fluid convection, simulation of metal foam processing, flow
NASA Astrophysics Data System (ADS)
Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred
2014-09-01
In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013), 10.1103/PhysRevE.88.013304] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.
Zhou, L; Qu, Z G; Ding, T; Miao, J Y
2016-04-01
The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems. PMID:27176384
Albernaz, Daniel; Do-Quang, Minh; Amberg, Gustav
2015-04-01
We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D(2) law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail. PMID:25974585
NASA Astrophysics Data System (ADS)
Albernaz, Daniel; Do-Quang, Minh; Amberg, Gustav
2015-04-01
We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D2 law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail.
Investigation of an entropic stabilizer for the lattice-Boltzmann method.
Mattila, Keijo K; Hegele, Luiz A; Philippi, Paulo C
2015-06-01
The lattice-Boltzmann (LB) method is commonly used for the simulation of fluid flows at the hydrodynamic level of description. Due to its kinetic theory origins, the standard LB schemes carry more degrees of freedom than strictly needed, e.g., for the approximation of solutions to the Navier-stokes equation. In particular, there is freedom in the details of the so-called collision operator. This aspect was recently utilized when an entropic stabilizer, based on the principle of maximizing local entropy, was proposed for the LB method [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)]. The proposed stabilizer can be considered as an add-on or extension to basic LB schemes. Here the entropic stabilizer is investigated numerically using the perturbed double periodic shear layer flow as a benchmark case. The investigation is carried out by comparing numerical results obtained with six distinct LB schemes. The main observation is that the unbounded, and not explicitly controllable, relaxation time for the higher-order moments will directly influence the leading-order error terms. As a consequence, the order of accuracy and, in general, the numerical behavior of LB schemes are substantially altered. Hence, in addition to systematic numerical validation, more detailed theoretical analysis of the entropic stabilizer is still required in order to properly understand its properties. PMID:26172795
NASA Astrophysics Data System (ADS)
Qing-Yu, Zhang; Dong-Ke, Sun; You-Fa, Zhang; Ming-Fang, Zhu
2016-06-01
In the present study, the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multi-component multi-phase lattice Boltzmann model. The results indicate that three typical nucleation modes of condensate droplets are produced by changing the geometrical parameters of nanoarrays. Droplets nucleated at the top (top-nucleation mode), or in the upside interpillar space of nanoarrays (side-nucleation mode), generate the non-wetting Cassie state, whereas the ones nucleated at the bottom corners between the nanoarrays (bottom-nucleation mode) present the wetting Wenzel state. Time evolutions of droplet pressures at the upside and downside of the liquid phase are analyzed to understand the wetting behaviors of the droplets condensed from different nucleation modes. The phenomena of droplet condensation on nanoarrays patterned with different hydrophilic and hydrophobic regions are simulated, indicating that the nucleation mode of condensate droplets can also be manipulated by modifying the local intrinsic wettability of nanoarray surface. The simulation results are compared well with the experimental observations reported in the literature. Project supported by the National Natural Science Foundation of China (Grant Nos. 51101035, 51371051, and 51306037).
An adaptive lattice Boltzmann scheme for modeling two-fluid-phase flow in porous medium systems
NASA Astrophysics Data System (ADS)
Dye, Amanda L.; McClure, James E.; Adalsteinsson, David; Miller, Cass T.
2016-04-01
We formulate a multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) to simulate two-fluid-phase flow in porous medium systems. The MRT LBM is applied to simulate the displacement of a wetting fluid by a nonwetting fluid in a system corresponding to a microfluidic cell. Analysis of the simulation shows widely varying time scales for the dynamics of fluid pressures, fluid saturations, and interfacial curvatures that are typical characteristics of such systems. Displacement phenomena include Haines jumps, which are relatively short duration isolated events of rapid fluid displacement driven by capillary instability. An adaptive algorithm is advanced using a level-set method to locate interfaces and estimate their rate of advancement. Because the displacement dynamics are confined to the interfacial regions for a majority of the relaxation time, the computational effort is focused on these regions. The proposed algorithm is shown to reduce computational effort by an order of magnitude, while yielding essentially identical solutions to a conventional fully coupled approach. The challenges posed by Haines jumps are also resolved by the adaptive algorithm. Possible extensions to the advanced method are discussed.
Lattice Boltzmann Simulation of Directed Assembly in Nano-Colloidal Systems
NASA Astrophysics Data System (ADS)
Abuzaid, Mohammad; Sun, Ying
2007-11-01
Suspensions of nano-sized colloids have received great attention for their broad applications in printable electronics, photonics, thin film processing, thermal management, etc. The properties of colloidal suspensions are often influenced by the interplay of the electrostatic repulsion, van der Waals attraction, depletion forces, hydrodynamic interaction, Brownian motion, diffusion, and gravity. In many applications, it is desirable to have ordered nanostructures, which can be achieved by electro-hydrodynamically directed particle assembly. In this paper, a Lattice Boltzmann scheme is used for direct numerical simulation of particle-particle and particle-field interactions in nano-colloidal systems under flow and electric fields. The interaction between particles and fluid is simulated via a mass conserving second-order bounce-back scheme. The aggregation rate of colloidal suspensions is investigated as a function of the fluid velocity and pressure, electric potential, electrode geometry, particle size and volume fraction, temperature, sedimentation effect, and other properties of both the particles and the carrier fluid. The influence of colloid size on various interaction forces is examined in detail. The design protocols for tuning colloidal suspensions under different electro-hydrodynamic field conditions are discussed for nanocrystalline thin film processing and nanofluids for thermal management.
Effect of interfacial layer on water flow in nanochannels: Lattice Boltzmann simulations
NASA Astrophysics Data System (ADS)
Jin, Yakang; Liu, Xuefeng; Liu, Zilong; Lu, Shuangfang; Xue, Qingzhong
2016-04-01
A novel interfacial model was proposed to understand water flow mechanism in nanochannels. Based on our pore-throat nanochannel model, the effect of interfacial layer on water flow in nanochannels was quantitatively studied using Lattice Boltzmann method (LBM). It is found that both the permeability of nanochannel and water velocity in the nanochannel dramatically decrease with increasing the thickness of interfacial layer. The permeability of nanochannel with pore radius of 10 nm decreases by about three orders of magnitude when the thickness of interfacial layer is changed from 0 nm to 3 nm gradually. Furthermore, it has been demonstrated that the cross-section shape has a great effect on the water flow inside nanochannel and the effect of interfacial layer on the permeability of nanochannel has a close relationship with cross-section shape when the pore size is smaller than 12 nm. Besides, both pore-throat ratio and throat length can greatly affect water flow in nanochannels, and the influence of interfacial layer on water flow in nanochannels becomes more evident with increasing pore-throat ratio and throat length. Our theoretical results provide a simple and effective method to study the flow phenomena in nano-porous media, particularly to quantitatively study the interfacial layer effect in nano-porous media.
Noise prediction of a subsonic turbulent round jet using the lattice-Boltzmann method
Lew, Phoi-Tack; Mongeau, Luc; Lyrintzis, Anastasios
2010-01-01
The lattice-Boltzmann method (LBM) was used to study the far-field noise generated from a Mach, Mj=0.4, unheated turbulent axisymmetric jet. A commercial code based on the LBM kernel was used to simulate the turbulent flow exhausting from a pipe which is 10 jet radii in length. Near-field flow results such as jet centerline velocity decay rates and turbulence intensities were in agreement with experimental results and results from comparable LES studies. The predicted far field sound pressure levels were within 2 dB from published experimental results. Weak unphysical tones were present at high frequency in the computed radiated sound pressure spectra. These tones are believed to be due to spurious sound wave reflections at boundaries between regions of varying voxel resolution. These “VR tones” did not appear to bias the underlying broadband noise spectrum, and they did not affect the overall levels significantly. The LBM appears to be a viable approach, comparable in accuracy to large eddy simulations, for the problem considered. The main advantages of this approach over Navier–Stokes based finite difference schemes may be a reduced computational cost, ease of including the nozzle in the computational domain, and ease of investigating nozzles with complex shapes. PMID:20815448
Lattice Boltzmann method for diffusion-limited partial dissolution of fluids.
Aursjø, Olav; Pride, Steven R
2015-07-01
A lattice Boltzmann model for two partially miscible fluids is developed. By partially miscible we mean that, although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region, each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit. We allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters. The approach is to define two regions within the fluid: one interfacial region having finite width, across which most of the concentration change occurs, and in which a surface tension force and color separation step are allowed for and one miscible fluid region where the concentration of the binary fluids follows an advection-diffusion equation and the mixture as a whole obeys the Navier-Stokes incompressible flow equations. Numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness. The model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to simulate a range of practical invasion problems such as injecting supercritical CO(2) into a porous material saturated with water for sequestration purposes. PMID:26274306
Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows.
Li, Q; Luo, K H; Gao, Y J; He, Y L
2012-02-01
The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions: one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this paper, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional force is included in the recovered momentum equation. The additional force has the following features. First, it is proportional to the macroscopic velocity. Second, it is zero in every single-phase region but is nonzero in the interface. Therefore it can be interpreted as an interfacial force. To investigate the effects of the additional interfacial force, numerical simulations are carried out for the problem of Rayleigh-Taylor instability, droplet splashing on a thin liquid film, and the evolution of a falling droplet under gravity. Numerical results demonstrate that, with the increase of the velocity or the Reynolds number, the additional interfacial force will gradually have an important influence on the interface and affect the numerical accuracy. PMID:22463354
Mixing and Transport in the Small Intestine: A Lattice-Boltzmann Model
NASA Astrophysics Data System (ADS)
Banco, Gino; Brasseur, James; Wang, Yanxing; Aliani, Amit; Webb, Andrew
2007-11-01
The two primary functions of the small intestine are absorption of nutrients into the blood stream and transport of material along the gut for eventual evacuation. The primary transport mechanism is peristalsis. The time scales for absorption, however, rely on mixing and transport of molecules between the bulk flow and epithelial surface. Two basic motions contribute to mixing: peristalsis and repetitive segmental contraction of short segments of the gut. In this study we evaluate the relative roles of peristalsis vs. segmental contraction on the degree of mixing and time scales of nutrient transport to the epithelium using a two-dimensional model of flow and mixing in the small intestine. The model uses the lattice-Boltzmann framework with second-order moving boundary conditions and passive scalar (Sc = 10). Segmental and peristaltic contractions were parameterized using magnetic resonance imaging data from rat models. The Reynolds numbers (1.9), segment lengths (33 mm), max radii (2.75 mm) and occlusion ratios (0.33) were matched for direct comparison. Mixing is quantified by the rate of dispersion of scalar from an initial concentration in the center of the segment. We find that radial mixing is more rapid with segmental than peristaltic motion, that radial dispersion is much more rapid than axial, and that axial is comparable between the motions.
NASA Astrophysics Data System (ADS)
Hiorth, A.; Jettestuen, E.; Cathles, L. M.; Madland, M. V.
2013-03-01
Pore water chemistry can dramatically affect the mechanical strength of chalk cores and the recovery of oil from them, but despite a great many core experiments, the mechanisms responsible remain unclear. This is in part because no single model is presently available that can address the changes in surface complexes and potential and mineral dissolution and precipitation that occur when fluids of different chemistry are injected. We report here the construction of a lattice Boltzmann model that includes non-linear dissolution-precipitation kinetics, surface complexation, and ion exchange. A link-based boundary condition which allows mineral boundaries to move and porosity to change is shown to converge to a correct representation of the macroscopic pore surface area. We show the chemical LB model developed predicts mineral dissolution and ion exchange similar to those predicted by PHREEQC for similar parameters, and we show how the methods developed can be applied to chalk core experiments where synthetic seawater is flooded through the core at 130 °C.
Lattice Boltzmann investigation of droplet inertial spreading on various porous surfaces
NASA Astrophysics Data System (ADS)
Frank, Xavier; Perré, Patrick; Li, Huai-Zhi
2015-05-01
The spreading of liquid drops on solid surfaces is a wide-spread phenomenon of both fundamental and industrial interest. In many applications, surfaces are porous and spreading patterns are very complex with respect to the case on smooth surfaces. Focusing on the inertial spreading just before the Tanner-like viscous regime, this work investigates the spreading of a low-viscosity droplet on a porous surface using lattice Boltzmann numerical simulations. The case of a flat surface is first considered, and it reveals a dependence on the solid equilibrium contact angle θse q, which is in good agreement with published experimental data. We conducted numerical experiments with various surfaces perforated by a regular pattern of holes of infinite length. The results show that the global spreading dynamics is independent of the porosity morphology. Through the assumption that, for wetting, the pores can be regarded as surface patches with a contact angle of θporee q=180∘ , we deduce an effective equilibrium contact angle θeffe q on the porous surface from the Cassie-Baxter law. A spreading model is then proposed to describe both a prefactor and an exponent that are similar to a flat surface whose equilibrium contact angle is θeffe q. This model compares satisfactorily with a large number of numerical experiments under varying conditions.
Lattice-Boltzmann Diesel Particulate Filter Sub-Grid Modeling - A Progress Report
Muntean, George G.; Rector, David R.; Herling, Darrell R.; Khaleel, Mohammad A.; Lessor, Delbert L.
2004-09-30
After treatment modeling capabilities are an important part of the diesel engine manufacturer's efforts to meet the quickly approaching EPA 2007 heavy-duty emissions regulations. A critical, yet poorly understood, component of particulate filter modeling is the representation of the soot oxidation rate. This term directly influences most of the macroscopic phenomenon of interest, including filtration efficiency, heat transfer, back pressure, and filter regeneration. Intrinsic soot cake properties such as packing density, permeability and heat transfer coefficients remain inadequately characterized (1). The work reported in this paper involves subgrid modeling techniques which may prove useful in resolving these inadequacies. The technique involves the use of a lattice Boltzmann modeling approach. This approach resolves length scales which are orders of magnitude below those typical of a standard computational fluid dynamics (CFD) representation of an aftertreatment device. The improved resolution may allow for the characterization of functionality not previously reported in the literature. This paper presents the first status report of this multiyear project. Descriptions of the modeling technique, the initial kinetics, and the development of the computational domain are provided. In addition, preliminary sample exercises are discussed in order to illustrate how the final model, once refined and validated, may be applied in practice.
NASA Astrophysics Data System (ADS)
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.
An adaptive lattice Boltzmann method for predicting turbulent wake fields in wind parks
NASA Astrophysics Data System (ADS)
Deiterding, Ralf; Wood, Stephen L.
2014-11-01
Wind turbines create large-scale wake structures that can affect downstream turbines considerably. Numerical simulation of the turbulent flow field is a viable approach in order to obtain a better understanding of these interactions and to optimize the turbine placement in wind parks. Yet, the development of effective computational methods for predictive wind farm simulation is challenging. As an alternative approach to presently employed vortex and actuator-based methods, we are currently developing a parallel adaptive lattice Boltzmann method for large eddy simulation of turbulent weakly compressible flows with embedded moving structures that shows good potential for effective wind turbine wake prediction. Since the method is formulated in an Eulerian frame of reference and on a dynamically changing nonuniform Cartesian grid, even moving boundaries can be considered rather easily. The presentation will describe all crucial components of the numerical method and discuss first verification computations. Among other configurations, simulations of the wake fields created by multiple Vesta V27 turbines will be shown.
NASA Astrophysics Data System (ADS)
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2016-04-01
The streaming potential phenomenon is produced by the flow of an electrolyte in a porous medium and is used for geophysical prospecting. It is quantified through an electrokinetic (EK) coefficient. The dependence of the EK coefficient on the conductivity of the electrolyte is described by the Helmholtz-Smoluchowski (HS) equation. This equation provides successful forecasts of the EK coefficient in the standard range of concentration. However, experimental measurements show deviations to this equation at extreme low and extreme high salinities. The aim of this study is to model the EK coefficient using Lattice Boltzmann simulations in a 2-D capillary channel, with a view to understanding these deviations. The effect of the constitutive parameters of the HS equation such as the permittivity and the viscosity is discussed. The validity of the HS equation using strong ζ potentials is assessed. Finally, a model of bulk fluid conductivity is derived. This model allows to take into account the change of local ionic distribution in the vicinity of the mineral. It appears to have a significant impact on the derivation of ζ potentials at low salinities and in the presence of polyvalent counterions.
A spectral-element discontinuous Galerkin lattice Boltzmann method for incompressible flows.
Min, M.; Lee, T.; Mathematics and Computer Science; City Univ. of New York
2011-01-01
We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.
Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces.
Li, Qing; Kang, Q J; Francois, M M; Hu, A J
2016-01-01
In this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated using a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D(2) law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowly inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet moving velocity. Furthermore, the processes that the Leidenfrost droplets climb uphill on inclined ratchet surfaces are also studied. Numerical results show that the maximum inclination angle at which a Leidenfrost droplet can still climb uphill successfully is affected by the initial radius of the droplet. PMID:26467921
Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces
NASA Astrophysics Data System (ADS)
Li, Qing; Kang, Q. J.; Francois, M. M.; Hu, A. J.
In this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowly inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet moving velocity. Furthermore, the processes that the Leidenfrost droplets climb uphill on inclined ratchet surfaces are also studied. Numerical results show that the maximum inclination angle at which a Leidenfrost droplet can still climb uphill successfully is affected by the initial radius of the droplet.
NASA Astrophysics Data System (ADS)
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2016-01-01
The streaming potential phenomenon is produced by the flow of an electrolyte in a porous medium, and is used for geophysical prospecting. It is quantified through an electrokinetic (EK) coefficient. The dependence of the EK coefficient on the conductivity of the electrolyte is described by the Helmholtz-Smoluchowski (HS) equation. This equation provides successful forecasts of the EK coefficient in the standard range of concentration. However, experimental measurements show deviations to this equation at extreme low and extreme high salinities. The aim of this study is to model the EK coefficient using Lattice Boltzmann simulations in a 2D capillary channel, with a view to understanding these deviations. The effect of the constitutive parameters of the HS equation such as the permittivity and the viscosity are discussed. The validity of the HS equation using strong ζ potentials is assessed. Finally, a model of bulk fluid conductivity is derived. This model allows to take into account the change of local ionic distribution in the vicinity of the mineral. It appears to have a significant impact on the derivation of ζ potentials at low salinities and in the presence of polyvalent counterions.
Lattice Boltzmann simulation of shale gas transport in organic nano-pores.
Zhang, Xiaoling; Xiao, Lizhi; Shan, Xiaowen; Guo, Long
2014-01-01
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale. PMID:24784022
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-28
Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less
Li, Q.; Kang, Q. J.; Francois, M. M.; He, Y. L.; Luo, K. H.
2015-03-03
A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach (Li et al., 2013). The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid–vapor phase change. Using the model, the liquid–vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic features and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Moreover, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies.
Li, Q.; Kang, Q. J.; Francois, M. M.; He, Y. L.; Luo, K. H.
2015-03-03
A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach (Li et al., 2013). The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid–vapor phase change. Using the model, the liquid–vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic featuresmore » and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Moreover, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies.« less
Reduction of the temperature jump in the immersed boundary-thermal lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Seta, Takeshi; Hayashi, Kosuke; Tomiyama, Akio
2015-11-01
We analytically and numerically investigate the boundary errors computed by the immersed boundary-thermal lattice Boltzmann method (IB-TLBM) with the two-relaxation-time (TRT) collision operator. In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. We derive the theoretical relation between the relaxation parameters for the symmetric and antisymmetric parts of the distribution function so as to eliminate the temperature jump. The simple TRT collision operator succeeds in reducing the temperature jump occurring at the high relaxation time in the IB-TLBM calculation. The porous plate problem numerically and analytically demonstrate that the velocity squared terms should be neglected in the equilibrium distribution function in order to eliminate the effect of the advection velocity on the temperature jump in the IB-TLBMs. The passive scalar model without the velocity squared terms more accurately calculates the incompressible temperature equation in the IB-TLBMs, compared to the double distribution model, which is based on the relation of the distribution function gk = (ek - u)2fk / 2 . We apply the passive scalar model without the velocity squared terms to the simulation of the natural convection between a hot circular cylinder and a cold square enclosure. The proposed method adequately sets the boundary values and provides reasonable average Nusselt numbers and maximum absolute values of the stream function.
Interface-capturing lattice Boltzmann equation model for two-phase flows
NASA Astrophysics Data System (ADS)
Lou, Qin; Guo, Zhaoli
2015-01-01
In this work, an interface-capturing lattice Boltzmann equation (LBE) model is proposed for two-phase flows. In the model, a Lax-Wendroff propagation scheme and a properly chosen equilibrium distribution function are employed. The Lax-Wendroff scheme is used to provide an adjustable Courant-Friedrichs-Lewy (CFL) number, and the equilibrium distribution is presented to remove the dependence of the relaxation time on the CFL number. As a result, the interface can be captured accurately by decreasing the CFL number. A theoretical expression is derived for the chemical potential gradient by solving the LBE directly for a two-phase system with a flat interface. The result shows that the gradient of the chemical potential is proportional to the square of the CFL number, which explains why the proposed model is able to capture the interface naturally with a small CFL number, and why large interface error exists in the standard LBE model. Numerical tests, including a one-dimensional flat interface problem, a two-dimensional circular droplet problem, and a three-dimensional spherical droplet problem, demonstrate that the proposed LBE model performs well and can capture a sharp interface with a suitable CFL number.
NASA Astrophysics Data System (ADS)
Wu, Jie; Huang, Jun-Jie
2015-07-01
Water management is one of the key issues in proton exchange membrane fuel cells. Fundamentally, it is related to dynamic behaviors of droplets on a gas diffusion layer (GDL) surface, and consequently they are investigated in this work. A two-dimensional hybrid method is employed to implement numerical simulations, in which the flow field is solved by using the lattice Boltzmann method and the interface between droplet and gas is captured by solving the Cahn-Hilliard equation directly. One or two liquid droplets are initially placed on the GDL surface of a gas channel, which is driven by the fully developed Poiseuille flow. At a fixed channel size, the effects of viscosity ratio of droplet to gas ( μ ∗ ), Capillary number (Ca, ratio of gas viscosity to surface tension), and droplet interaction on the dynamic behaviors of droplets are systematically studied. By decreasing viscosity ratio or increasing Capillary number, the single droplet can detach from the GDL surface easily. On the other hand, when two identical droplets stay close to each other or a larger droplet is placed in front of a smaller droplet, the removal of two droplets is promoted.
Lattice Boltzmann simulation of turbulence-induced flocculation of cohesive sediment
NASA Astrophysics Data System (ADS)
Zhang, Jin-Feng; Zhang, Qing-He; Maa, Jerome P.-Y.; Qiao, Guang-Quan
2013-10-01
Both the floc formation and floc breakup of cohesive sediment are affected by turbulent shear which is recognized as one of the most important parameters, and thus, on the settling and transport of cohesive sediment. In this study, the development of floc characteristics at early stage and steady-state of flocculation were investigated via a three-dimensional lattice Boltzmann numerical model for turbulence-induced flocculation. Simulations for collision and aggregation of various size particles, floc growth, and breakup in isotropic and homogenous turbulent flows with different shear stresses were conducted. Model results for the temporal evolution of floc size distribution show that the normalized floc size distributions is time-independent during early stage of flocculation, and at steady-state, shear rate has no effect on the shape of normalized floc size distribution. Furthermore, the size, settling velocity, and effective density of flocs at the non-equilibrium flocculation stage do not change significantly for shear stresses in the range 0-0.4 N m-2. The relationships between floc size and settling velocity established during floc growth stages and that during steady-states are different.
Sun, Chenghai; Migliorini, Cristiano; Munn, Lance L
2003-07-01
Leukocyte rolling on the vascular endothelium requires initial contact between leukocytes circulating in the blood and the vessel wall. Although specific adhesion mechanisms are involved in leukocyte-endothelium interactions, adhesion patterns in vivo suggest other rheological mechanisms also play a role. Previous studies have proposed that the abundance of leukocyte rolling in postcapillary venules is due to interactions between red blood cells (RBCs) and leukocytes as they enter postcapillary expansions, but the details of the fluid dynamics have not been elucidated. We have analyzed the interactions of red and white blood cells as they flow from a capillary into a postcapillary venule using a lattice Boltzmann approach. This technique provides the complete solution of the flow field and quantification of the particle-particle forces in a relevant geometry. Our results show that capillary-postcapillary venule diameter ratio, RBC configuration, and RBC shape are critical determinants of the initiation of cell rolling in postcapillary venules. The model predicts that an optimal configuration of the trailing red blood cells is required to drive the white blood cell to the wall. PMID:12829477
Lattice Boltzmann simulation of heat transfer and fluid flow in a microchannel with nanofluids
NASA Astrophysics Data System (ADS)
Yang, Yue-Tzu; Lai, Feng-Hsiang
2011-10-01
Mathematical modeling is performed to simulate forced convection flow of 47 nm- Al2O3/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Single channel flow and conjugate heat transfer problem are taken into consideration and the heat transfer rate using a nanofluid is examined. Simulations are conducted at low Reynolds numbers (2 ≤ Re ≤ 16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range of 0.6 le overline{Nu} le 13 . Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for practical applications.
Evaluation of the unstructured lattice Boltzmann method in porous flow simulations
NASA Astrophysics Data System (ADS)
Misztal, Marek; Matin, Rastin; Hernandez, Anier; Mathiesen, Joachim
2015-11-01
Flows in porous media are among the most challenging to simulate using the computational fluid dynamics methods, primarily due to the complex boundaries, often characterized by a very broad distribution of pore sizes. The standard (regular grid based) lattice Boltzmann method with the multi-relaxation time (MRT) collision operator is often used to simulate such flows. However, due to the lack of coupling between the positions of the computational grid nodes and the solid boundaries, the properties of the simulated flow might unnaturally vary with the fluid's viscosity, depending on the parameters of the MRT operator. This is, for instance, the case with the otherwise popular, single-relaxation time Bhatnagar-Gross-Krook (BGK) collision operator. Our focus has been on the unstructured grid based, finite element variant of the LBM. By using such approach, we can place the computational grid nodes precisely at the solid boundary. Since there is no prior work on the accuracy of this method in simulating porous flows, we perform a thorough permeability study using both BGK and MRT operators at a wide range of viscosities. We benchmark these models on artificial samples with known solutions, and further, we demonstrate the findings of our studies in the porous networks of real rocks. Predicting Petrophysical Parameters: A Project Sponsored by HTF and Maersk Oil and Gas.
Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces
NASA Astrophysics Data System (ADS)
Mazloomi M., Ali; Chikatamarla, Shyam S.; Karlin, Iliya V.
2015-08-01
The recently introduced entropic lattice Boltzmann model (ELBM) for multiphase flows [A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015), 10.1103/PhysRevLett.114.174502] is extended to the simulation of dynamic fluid-solid interface problems. The thermodynamically consistent, nonlinearly stable ELBM together with a polynomial representation of the equation of state enables us to investigate the dynamics of the contact line in a wide range of applications, from capillary filling to liquid drop impact onto a flat surfaces with different wettability. The static interface behavior is tested by means of the liquid column in a channel to verify the Young-Laplace law. The numerical results of a capillary filling problem in a channel with wettability gradient show an excellent match with the existing analytical solution. Simulations of drop impact onto both wettable and nonwettable surfaces show that the ELBM reproduces the experimentally observed drop behavior in a quantitative manner. Results reported herein demonstrate that the present model is a promising alternative for studying the vapor-liquid-solid interface dynamics.
Development of a Lattice Boltzmann Framework for Numerical Simulation of Thrombosis
NASA Astrophysics Data System (ADS)
Harrison, S. E.; Bernsdorf, J.; Hose, D. R.; Lawford, P. V.
The interacting factors relating to thrombogenesis were defined by Virchow in 1856 to be abnormalities of blood chemistry, the vessel wall and haemodynamics. Together, these factors are known as Virchow's triad. Many attempts have been made to simulate numerically certain aspects of the complex phenomena of thrombosis, but a comprehensive model, which includes the biochemical and physical aspects of Virchow's triad, and is capable of predicting thrombus development within physiological geometries has not yet been developed. Such a model would consider the role of platelets and the coagulation cascade along with the properties of the flow in the chosen vessel. A lattice Boltzmann thrombosis framework has been developed, on top of an existing flow solver, to model the formation of thrombi resulting from platelet activation and initiation of the coagulation cascade by one or more of the strands of Virchow's triad. Both processes then act in parallel, to restore homeostasis as the deposited thrombus disturbs the flow. Results are presented in a model of deep vein thrombosis (DVT), resulting from hypoxia and associated endothelial damage.
Modified momentum exchange method for fluid-particle interactions in the lattice Boltzmann method.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-03-01
In this paper, a modified momentum exchange method for fluid-particle interactions is proposed based on the finite-volume lattice Boltzmann method. The idea of the improvement is to remove the restriction that the boundary points must be set as the midpoints of the grid lines or the intersection of the grid lines with the solid boundaries. The particle surface is represented by a set of arc (area) elements, and the interior fluid is used which the geometric conservation law is naturally satisfied. The interactions between fluid and arc (area) elements of particle boundary are considered using the momentum exchange method, and the mass of the fluid particles which collide with an arc (area) element is obtained by means of numerical integration in the control volume. The fluid field is corrected with the help of the smooth kernel function. Moreover, a generalized explicit time marching scheme is introduced to resolve the motion of particle in the problems with the ratio of particle density to fluid density is close to or less than 1. Finally, some numerical case studies of particle sedimentation are carried out to validate the present method. The corresponding results have a good agreement with the previous literature, which strongly demonstrates the capability of the improved method. PMID:25871240
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility. PMID:16383571
Lattice-Boltzmann modeling of micromodel experiments representing a CO2-brine system
Porter, Mark L; Kang, Qinjun; Tarimala, Sowmitri; Abdel - Fattah, Amr I; Backhaus, Scott; Carey, James W
2010-12-21
Successful sequestration of CO{sub 2} into deep saline aquifers presents an enormous challenge that requires fundamental understanding of reactive-multi phase flow and transport across many temporal and spatial scales. Of critical importance is accurately predicting the efficiency of CO{sub 2} trapping mechanisms. At the pore scale (e.g., microns to millimeters) the interfacial area between CO{sub 2} and brine, as well as CO{sub 2} and the solid phase, directly influences the amount of CO{sub 2} trapped due to capillary forces, dissolution and mineral precipitation. In this work, we model immiscible displacement micromodel experiments using the lattice-Boltzmann (LB) method. We focus on quantifying interfacial area as a function of capillary numbers and viscosity ratios typically encountered in CO{sub 2} sequestration operations. We show that the LB model adequately predicts the steady-state experimental flow patterns and interfacial area measurements. Based on the steady-state agreement, we use the LB model to investigate interfacial dynamics (e.g., fluid-fluid interfacial velocity and the rate of production of fluid-fluid interfacial area). In addition, we quantify the amount of interfacial area and the interfacial dynamics associated with the capillary trapped nonwetting phase. This is expected to be important for predicting the amount of nonwetting phase subsequently trapped due to dissolution and mineral precipitation.
Role of ions in thermal diffusion of DNA: Lattice Boltzmann based simulations
NASA Astrophysics Data System (ADS)
Hammack, Audrey; Rana, Daharsh; May, Karl; Bledsoe, Matthew; Kreft Pearce, Jennifer; Chen, Yeng-Long
2008-11-01
The Ludwig-Soret effect, the migrarion of a species as a consequence of a temperature gradient, has been a factor in the development of microfluidic laboratory instrumentation. In a system consisting of DNA in a buffered salt solution exposed to a temperature gradient in micro channels, it has previously been observed that DNA will migrate to the colder regions, yielding an irregular density profile. We present a computational model in order to quantify the motion of the particles and describe the causes of this migration. In this construct, the salt ions are modeled as charged point particles and DNA as charged beads connected by springs. The motions of particles is calculated by using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the salt are also affected by the temperature gradient, creating a density profile. By varying the number of ions, the charge of the ions and the length of the DNA chain, we observe that the accumulation of ions in the cold region enhances the migration of the DNA to those regions of the channel.
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-28
Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
NASA Astrophysics Data System (ADS)
Zheng, Lin; Zheng, Song; Zhai, Qinglan
2016-02-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results.
NASA Astrophysics Data System (ADS)
Dubov, Alexander L.; Schmieschek, Sebastian; Asmolov, Evgeny S.; Harting, Jens; Vinogradova, Olga I.
2014-01-01
By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area ϕ. For very large values of h/R, we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R = O(1), the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, h ≪ R the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing ϕ. In the limit of very small separations, our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with ϕ = 0.5.
Study for optical manipulation of a surfactant-covered droplet using lattice Boltzmann method
Choi, Se Bin; Kondaraju, Sasidhar; Sang Lee, Joon
2014-01-01
In this study, we simulated deformation and surfactant distribution on the interface of a surfactant-covered droplet using optical tweezers as an external source. Two optical forces attracted a single droplet from the center to both sides. This resulted in an elliptical shape deformation. The droplet deformation was characterized as the change of the magnitudes of surface tension and optical force. In this process, a non-linear relationship among deformation, surface tension, and optical forces was observed. The change in the local surfactant concentration resulting from the application of optical forces was also analyzed and compared with the concentration of surfactants subjected to an extensional flow. Under the optical force influence, the surfactant molecules were concentrated at the droplet equator, which is totally opposite to the surfactants behavior under extensional flow, where the molecules were concentrated at the poles. Lastly, the quasi-equilibrium surfactant distribution was obtained by combining the effects of the optical forces with the extensional flow. All simulations were executed by the lattice Boltzmann method which is a powerful tool for solving micro-scale problems. PMID:24753737
Khajepor, Sorush; Chen, Baixin
2016-01-01
A method is developed to analytically and consistently implement cubic equations of state into the recently proposed multipseudopotential interaction (MPI) scheme in the class of two-phase lattice Boltzmann (LB) models [S. Khajepor, J. Wen, and B. Chen, Phys. Rev. E 91, 023301 (2015)]10.1103/PhysRevE.91.023301. An MPI forcing term is applied to reduce the constraints on the mathematical shape of the thermodynamically consistent pseudopotentials; this allows the parameters of the MPI forces to be determined analytically without the need of curve fitting or trial and error methods. Attraction and repulsion parts of equations of state (EOSs), representing underlying molecular interactions, are modeled by individual pseudopotentials. Four EOSs, van der Waals, Carnahan-Starling, Peng-Robinson, and Soave-Redlich-Kwong, are investigated and the results show that the developed MPI-LB system can satisfactorily recover the thermodynamic states of interest. The phase interface is predicted analytically and controlled via EOS parameters independently and its effect on the vapor-liquid equilibrium system is studied. The scheme is highly stable to very high density ratios and the accuracy of the results can be enhanced by increasing the interface resolution. The MPI drop is evaluated with regard to surface tension, spurious velocities, isotropy, dynamic behavior, and the stability dependence on the relaxation time. PMID:26871187
NASA Astrophysics Data System (ADS)
Khajepor, Sorush; Chen, Baixin
2016-01-01
A method is developed to analytically and consistently implement cubic equations of state into the recently proposed multipseudopotential interaction (MPI) scheme in the class of two-phase lattice Boltzmann (LB) models [S. Khajepor, J. Wen, and B. Chen, Phys. Rev. E 91, 023301 (2015)], 10.1103/PhysRevE.91.023301. An MPI forcing term is applied to reduce the constraints on the mathematical shape of the thermodynamically consistent pseudopotentials; this allows the parameters of the MPI forces to be determined analytically without the need of curve fitting or trial and error methods. Attraction and repulsion parts of equations of state (EOSs), representing underlying molecular interactions, are modeled by individual pseudopotentials. Four EOSs, van der Waals, Carnahan-Starling, Peng-Robinson, and Soave-Redlich-Kwong, are investigated and the results show that the developed MPI-LB system can satisfactorily recover the thermodynamic states of interest. The phase interface is predicted analytically and controlled via EOS parameters independently and its effect on the vapor-liquid equilibrium system is studied. The scheme is highly stable to very high density ratios and the accuracy of the results can be enhanced by increasing the interface resolution. The MPI drop is evaluated with regard to surface tension, spurious velocities, isotropy, dynamic behavior, and the stability dependence on the relaxation time.
NASA Astrophysics Data System (ADS)
Chau, J. F.; Or, D.; Jones, S.; Sukop, M.
2004-05-01
Liquid distribution in unsaturated porous media under different gravitational forces and resulting gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. Different fluid behavior in plant growth media under microgravity conditions as compared to earth presents a challenge to plant growth in long duration space exploration missions. Our primary objective was to provide qualitative description and quantitative measures of the role of reduced gravity on hydraulic and gaseous transport properties in simulated porous media. We implemented a multi-phase lattice Boltzmann code for equilibrium distribution of liquid in an idealized two-dimensional porous medium under microgravity and "normal" gravity conditions. The information was then used to provide boundary conditions for simulation of gaseous diffusion through the equilibrium domains (considering diffusion through liquid phase negligibly small). The models were tested by comparison with several analytical solutions to the diffusion equation, with excellent results. The relative diffusion coefficient for both series of simulations (with and without gravity) as functions of air-filled porosity was in good agreement with established models of Millington-Quirk. Liquid distribution under earth's gravity featured increased water content at the lower part of the medium relative to the distribution in reduced gravity, which resulted in decreased gas diffusion through a vertically oriented column of a porous medium. Simulation results for larger domains under various orientations will be presented.
Hydrodynamic instabilities of near-critical CO2 flow in microchannels: Lattice Boltzmann simulation
NASA Astrophysics Data System (ADS)
Holdych, D. J.; Georgiadis, J. G.; Buckius, R. O.
2004-05-01
Motivated by systematic CO2 evaporation experiments which recently became available (J. Pettersen, "Flow vaporization of CO2 in microchannel tubes," Doctor technicae thesis, Norwegian University of Science and Technology, 2002), the present work constitutes an exploratory investigation of isothermal flow of CO2 near its liquid-vapor critical point through a long 5 μm diameter microchannel. A modified van der Waals constitutive model—with properties closely approximating those of "real" near-critical CO2—is incorporated in a two-dimensional lattice Boltzmann hydrodynamics model by embedding a dimensionless parameter X, with X→1 denoting the "real" fluid. The hydrodynamic phenomena resulting by imposing a constant pressure gradient along a periodic channel are investigated by considering two regimes in tandem: (1) transition from bubbly to annular flow with a liquid film formed at the channel walls and (2) destabilization of the liquid film by the Kelvin-Helmholtz instability. Due to numerical constraints, intrinsic modeling errors are introduced and are shown to be associated with discrepancies in the relative vapor-liquid interfacial thickness, which is expressed by X. The effects of these errors are investigated both theoretically and numerically in the physical limit X→1. Numerically determined flow patterns compare qualitatively well with direct visualization results obtained by Pettersen. Overall, the characteristics of isothermal near-critical two-phase flow in microchannels can be reproduced by the appropriate modification of the thermophysical properties of CO2.
NASA Astrophysics Data System (ADS)
Zhou, L.; Qu, Z. G.; Ding, T.; Miao, J. Y.
2016-04-01
The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.
Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders
NASA Astrophysics Data System (ADS)
Mussa, Alberto; Asinari, Pietro; Luo, Li-Shi
2009-03-01
We apply the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model to simulate laminar flows in two-dimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched non-uniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of non-uniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRT-LBE. The MRT-LBE with non-uniform stretched grids is first validated with a number of test cases: the Poiseuille flow, the flow past a cylinder asymmetrically placed in a channel, and the flow past a cylinder in an unbounded domain. We use the LBE method to simulate the flow past two tandem cylinders in an unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRT-LBE method with grid stretching.
Lattice Boltzmann method for short-pulsed laser transport in a multi-layered medium
NASA Astrophysics Data System (ADS)
Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping
2015-04-01
We construct a lattice Boltzmann method (LBM) for transient radiative transfer in one-dimensional multi-layered medium with distinct refractive index in each layer. The left boundary is irradiated normally by a short-pulsed laser. The Fresnel interfaces conditions, which incorporate reflection and refraction, are used at the boundaries and the interfaces. Based on the Fresnel's law and Snell's law, the interfacial intensity formulas are introduced. The collimated and diffuse intensities are treated individually. At a transient time step, the collimated component is first solved by LBM and then embedded into the transient radiative transfer equation as a source term. To keep the consistency of the directions in all the layers, angular interpolation of the intensities at the interfaces is adopted. The transient radiative transfer in a two-layer medium is first investigated, and the time-resolved results are validated by comparing with those by the Monte Carlo method (MCM). Of particular interest, the angular intensities along the slab at different times are presented to illustrate a variety of interesting phenomena, and the discontinuous nature of the intensity at the interfaces is discussed. The effects of various parameters on the time-resolved signals are examined.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
Yong, Wen-An; Zhao, Weifeng; Luo, Li-Shi
2016-03-01
We propose using the Maxwell iteration to derive the hydrodynamic equations from the lattice Boltzmann equation (LBE) with an external forcing term. The proposed methodology differs from existing approaches in several aspects. First, it need not explicitly introduce multiple-timescales or the Knudsen number, both of which are required in the Chapman-Enskog analysis. Second, it need not use the Hilbert expansion of the hydrodynamic variables, which is necessary in the asymptotic analysis of the LBE. The proposed methodology assumes the acoustic scaling (or the convective scaling) δ_{t}∼δ_{x}, thus δ_{t} is the only expansion parameter in the analysis of the LBE system, and it leads to the Navier-Stokes equations in compressible form. The forcing density derived in this work can reproduce existing forcing schemes by adjusting appropriate parameters. The proposed methodology also analyzes the numerical accuracy of the LBE. In particular, it shows the Mach number Ma should scale as O(δ_{t}^{1/3}) to maintain the truncation errors due to Ma and δ_{t} in balance when δ_{t}→0, so that the LBE can converge to the expected hydrodynamic equations effectively and efficiently. PMID:27078487
NASA Astrophysics Data System (ADS)
Yong, Wen-An; Zhao, Weifeng; Luo, Li-Shi
2016-03-01
We propose using the Maxwell iteration to derive the hydrodynamic equations from the lattice Boltzmann equation (LBE) with an external forcing term. The proposed methodology differs from existing approaches in several aspects. First, it need not explicitly introduce multiple-timescales or the Knudsen number, both of which are required in the Chapman-Enskog analysis. Second, it need not use the Hilbert expansion of the hydrodynamic variables, which is necessary in the asymptotic analysis of the LBE. The proposed methodology assumes the acoustic scaling (or the convective scaling) δt˜δx , thus δt is the only expansion parameter in the analysis of the LBE system, and it leads to the Navier-Stokes equations in compressible form. The forcing density derived in this work can reproduce existing forcing schemes by adjusting appropriate parameters. The proposed methodology also analyzes the numerical accuracy of the LBE. In particular, it shows the Mach number Ma should scale as O (δt1 /3) to maintain the truncation errors due to Ma and δt in balance when δt→0 , so that the LBE can converge to the expected hydrodynamic equations effectively and efficiently.
Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect
NASA Astrophysics Data System (ADS)
Chen, Li; Fang, Wenzhen; Kang, Qinjun; De'Haven Hyman, Jeffrey; Viswanathan, Hari S.; Tao, Wen-Quan
2015-03-01
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002), 10.1103/PhysRevE.65.046308]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999), 10.1080/108939599199864 and F. Civan, Transp. Porous Med. 82, 375 (2010), 10.1007/s11242-009-9432-z] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.
Lattice Boltzmann simulations of sedimentation of a single fiber in a weak vertical shear flow
NASA Astrophysics Data System (ADS)
Qi, Dewei; He, Guowei; Liu, Yingming
2013-09-01
Instability of a suspension is directly related to the problem of the cross-stream migration of a particle relative to its neighboring particle suspension. Such cross-stream or lateral migration of a single non-spherical particle (fiber) settling in a bounded weak shear flow with vertical streamlines produced by a perturbation to the fiber number density is studied using lattice Boltzmann simulations. The present simulation results demonstrate that at a given shear rate, the lateral migration can be divided into three phases depending on settling Reynolds number Rsd and particle aspect ratio κ. At a low settling Reynolds number Rsd, the suspension becomes more stable in phase 1. As Rsd increases and excesses a critical settling Reynolds number Rsd1, the fiber suspension becomes unstable in phase 2. In phase 3, at an enough large Rsd, the inertia dominates the weak shear flow and it may have little effect on stability. A mechanism of the instability induced by an inertial fiber orientation drift and a shear induced cross-streamline drift, recently proposed by Shin, Koch, and Subramanian ["Structure and dynamics of dilute suspensions of finite reynolds number settling fibers," Phys. Fluids 21, 123304 (2009)], is examined and confirmed.
NASA Astrophysics Data System (ADS)
Deiterding, Ralf; Wood, Stephen L.
2015-11-01
Operating horizontal axis wind turbines create large-scale turbulent wake structures that affect the power output of downwind turbines considerably. The computational prediction of this phenomenon is challenging as efficient low dissipation schemes are necessary that represent the vorticity production by the moving structures accurately and are able to transport wakes without significant artificial decay over distances of several rotor diameters. We have developed the first version of a parallel adaptive lattice Boltzmann method for large eddy simulation of turbulent weakly compressible flows with embedded moving structures that considers these requirements rather naturally and enables first principle simulations of wake-turbine interaction phenomena at reasonable computational costs. The presentation will describe the employed algorithms and present relevant verification and validation computations. For instance, power and thrust coefficients of a Vestas V27 turbine are predicted within 5% of the manufacturer's specifications. Simulations of three Vestas V27-225kW turbines in triangular arrangement analyze the reduction in power production due to upstream wake generation for different inflow conditions.
Audigier, Chloé; Mansi, Tommaso; Delingette, Hervé; Rapaka, Saikiran; Mihalef, Viorel; Sharma, Puneet; Carnegie, Daniel; Boctor, Emad; Choti, Michael; Kamen, Ali; Comaniciu, Dorin; Ayache, Nicholas
2013-01-01
Radio-frequency ablation (RFA), the most widely used minimally invasive ablative therapy of liver cancer, is challenged by a lack of patient-specific planning. In particular, the presence of blood vessels and time-varying thermal diffusivity makes the prediction of the extent of the ablated tissue difficult. This may result in incomplete treatments and increased risk of recurrence. We propose a new model of the physical mechanisms involved in RFA of abdominal tumors based on Lattice Boltzmann Method to predict the extent of ablation given the probe location and the biological parameters. Our method relies on patient images, from which level set representations of liver geometry, tumor shape and vessels are extracted. Then a computational model of heat diffusion, cellular necrosis and blood flow through vessels and liver is solved to estimate the extent of ablated tissue. After quantitative verifications against an analytical solution, we apply our framework to 5 patients datasets which include pre- and post-operative CT images, yielding promising correlation between predicted and actual ablation extent (mean point to mesh errors of 8.7 mm). Implemented on graphics processing units, our method may enable RFA planning in clinical settings as it leads to near real-time computation: 1 minute of ablation is simulated in 1.14 minutes, which is almost 60x faster than standard finite element method. PMID:24505777
Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Huang, Haibo; Wu, YanFeng; Lu, Xiyun
2012-10-01
The intrinsic viscosities for prolate and oblate spheroidal suspensions in a dilute Newtonian fluid are studied using a three-dimensional lattice Boltzmann method. Through directly calculated viscous dissipation, the minimum and maximum intrinsic viscosities and the period of the tumbling state all agree well with the analytical solution for particles with different aspect ratios. This numerical test verifies the analysis on maximum and minimum intrinsic viscosities. Different behavior patterns of transient intrinsic viscosity in a period are analyzed in detail. A phase lag between the transient intrinsic viscosity and the orientation of the particle at finite Reynolds number (Re) is found and attributed to fluid and particle inertia. At lower Re, the phase lag increases with Re. There exists a critical Reynolds number Rea at which the phase lag begins to decrease with Re. The Rea depends on the aspect ratio of the particle. We found that both the intrinsic viscosity and the period change linearly with Re when Re
Red Blood Cells Initiate Leukocyte Rolling in Postcapillary Expansions: A Lattice Boltzmann Analysis
Sun, Chenghai; Migliorini, Cristiano; Munn, Lance L.
2003-01-01
Leukocyte rolling on the vascular endothelium requires initial contact between leukocytes circulating in the blood and the vessel wall. Although specific adhesion mechanisms are involved in leukocyte-endothelium interactions, adhesion patterns in vivo suggest other rheological mechanisms also play a role. Previous studies have proposed that the abundance of leukocyte rolling in postcapillary venules is due to interactions between red blood cells (RBCs) and leukocytes as they enter postcapillary expansions, but the details of the fluid dynamics have not been elucidated. We have analyzed the interactions of red and white blood cells as they flow from a capillary into a postcapillary venule using a lattice Boltzmann approach. This technique provides the complete solution of the flow field and quantification of the particle-particle forces in a relevant geometry. Our results show that capillary-postcapillary venule diameter ratio, RBC configuration, and RBC shape are critical determinants of the initiation of cell rolling in postcapillary venules. The model predicts that an optimal configuration of the trailing red blood cells is required to drive the white blood cell to the wall. PMID:12829477
Application of the multi distribution function lattice Boltzmann approach to thermal flows
NASA Astrophysics Data System (ADS)
Parmigiani, A.; Huber, C.; Chopard, B.; Latt, J.; Bachmann, O.
2009-04-01
Numerical methods able to model high Rayleigh ( Ra) and high Prandtl ( Pr) number thermal convection are important to study large-scale geophysical phenomena occuring in very viscous fluids such as magma chamber dynamics (104 < Pr < 107 and 107 < Ra < 1011). The important variable to quantify the thermal state of a convective fluid is a generalized dimensionless heat transfer coefficient (the Nusselt number) whose measure indicates the relative efficiency of the thermal convection. In this paper we test the ability of Multi-distribution Function approach (MDF) Thermal Lattice Boltzmann method to study the well-established scaling result for the Nusselt number ( Nu ∝ Ra 1/3) in Rayleigh Bénard convection for 104 ≤ Ra ≤ 109 and 101 ≤ Pr ≤ 104. We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time N c required for the algorithm to converge and (2) high spatial accuracy needed to resolve the thickness of thermal plumes and both thermal and velocity boundary layer. We try to decrease the computational demands of the method using a multiscale approach based on the implicit dependence of the Pr number on the relaxation time, the spatial and temporal resolution characteristic of the MDF thermal model.
Shrinkage of bubbles and drops in the lattice Boltzmann equation method for nonideal gases.
Zheng, Lin; Lee, Taehun; Guo, Zhaoli; Rumschitzki, David
2014-03-01
One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial region has a finite (i.e., noninfinitesimal) thickness known as a diffuse interface. In simulations of, e.g., bubble or drop dynamics, for problems involving nonideal gases, one frequently observes that the diffuse interface method produces a spontaneous, nonphysical shrinkage of the bubble or drop radius. In this paper, we analyze in detail a single-fluid two-phase model and use a LBE model for nonideal gases in order to explain this fundamental problem. For simplicity, we only investigate the static bubble or droplet problem. We find that the method indeed produces a density shift, bubble or droplet shrinkage, as well as a critical radius below which the bubble or droplet eventually vanishes. Assuming that the ratio between the interface thickness D and the initial bubble or droplet radius r0 is small, we analytically show the existence of this density shift, bubble or droplet radius shrinkage, and critical bubble or droplet survival radius. Numerical results confirm our analysis. We also consider droplets on a solid surface with different curvatures, contact angles, and initial droplet volumes. Numerical results show that the curvature, contact angle, and the initial droplet volume have an effect on this spontaneous shrinkage process, consistent with the survival criterion. PMID:24730962
Simulations of the Karlsruhe Dynamo Using the Lattice-Boltzmann Method
NASA Astrophysics Data System (ADS)
Sarkar, Aveek
2005-07-01
The dynamo mechanism is on the way of understanding. Several numerical simul ations have shown the dynamo mechanism successfully. In recent years dynamo mech anism could be brought down to the laboratory even, where self-sustained magneti c field is observed (fed by the kinetic energy of the fluid, as predicted in the theory). One of these successful laboratory experiments is situated in Karlsruhe, Germany. Even though the magnetic field is self sustained in the experiment, the magn etic field oscillation around its mean value is still to be discovered. Simulations of the dynamo effect require the simultaneous integration of the Navier-Stokes equation and of the Induction equation of electrodynamics. We dev elop a hybrid method in which the Navier-Stokes equation is solved with a Lattic e-Boltzmann method and the Induction equation is treated with a spectral method. Later, this hybrid code is used to simulate the Karlsruhe Dynamo experiment and we suggest the cause of the magnetic field oscillation in this thesis. Die Dynamoeinheit ist auf der Weise des Verstehens. Einige numerische simul ations haben die Dynamoeinheit erfolgreich gezeigt. In den letzten Jahren Dynamo könnte mech anism zum Labor sogar gesenkt werden, wo Selbst-unterstütztes magnetic wird beobachtet auffangen (eingezogen durch die kinetische Energie der Flüssigkeit, wie in der Theorie vorausgesagt). Eins dieser erfolgreichen Laborexperimente wird in Karlsruhe, Deutschland aufgestellt. Numerisch versuchen wir, diesen Dynamo zu simulieren.
Capillary filling and Haines jump dynamics using free energy Lattice Boltzmann simulations
NASA Astrophysics Data System (ADS)
Zacharoudiou, Ioannis; Boek, Edo S.
2016-06-01
We investigate numerically the dynamics of capillary filling and Haines jump events using free energy Lattice Boltzmann (LB) simulations. Both processes are potentially important multi-phase pore-scale flow processes for geological CO2 sequestration and oil recovery. We first focus on capillary filling and demonstrate that the numerical method can capture the correct dynamics in the limit of long times for both high and low viscosity ratios, i.e. the method gives the correct scaling for the length of the penetrating fluid column as a function of time. Examining further the early times of capillary filling, three consecutive length vs. time regimes have been observed, in agreement with available experimental work in the literature. In addition, we carry out simulations of Haines jump events in idealised and realistic rock pore geometries. We observe that the Haines jump events are cooperative, non-local and associated with both drainage and imbibition dynamics. Our observations show that the pore filling dynamics is controlled by the Ohnesorge number, associated with the balance between viscous forces and inertial / surface tension forces. Using this concept, we are able to identify the type of pore filling dynamics that will occur.
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247
Evaluation of Airframe Noise Reduction Concepts via Simulations Using a Lattice Boltzmann Approach
NASA Technical Reports Server (NTRS)
Fares, Ehab; Casalino, Damiano; Khorrami, Mehdi R.
2015-01-01
Unsteady computations are presented for a high-fidelity, 18% scale, semi-span Gulfstream aircraft model in landing configuration, i.e. flap deflected at 39 degree and main landing gear deployed. The simulations employ the lattice Boltzmann solver PowerFLOW® to simultaneously capture the flow physics and acoustics in the near field. Sound propagation to the far field is obtained using a Ffowcs Williams and Hawkings acoustic analogy approach. In addition to the baseline geometry, which was presented previously, various noise reduction concepts for the flap and main landing gear are simulated. In particular, care is taken to fully resolve the complex geometrical details associated with these concepts in order to capture the resulting intricate local flow field thus enabling accurate prediction of their acoustic behavior. To determine aeroacoustic performance, the farfield noise predicted with the concepts applied is compared to high-fidelity simulations of the untreated baseline configurations. To assess the accuracy of the computed results, the aerodynamic and aeroacoustic impact of the noise reduction concepts is evaluated numerically and compared to experimental results for the same model. The trends and effectiveness of the simulated noise reduction concepts compare well with measured values and demonstrate that the computational approach is capable of capturing the primary effects of the acoustic treatment on a full aircraft model.
Carter, Jonathan; Oliker, Leonid
2006-01-09
The last decade has witnessed a rapid proliferation of superscalarcache-based microprocessors to build high-end computing (HEC) platforms, primarily because of their generality, scalability, and cost effectiveness. However, the growing gap between sustained and peak performance for full-scale scientific applications on such platforms has become major concern in high performance computing. The latest generation of custom-built parallel vector systems have the potential to address this concern for numerical algorithms with sufficient regularity in their computational structure. In this work, we explore two and three dimensional implementations of a lattice-Boltzmann magnetohydrodynamics (MHD) physics application, on some of today's most powerful supercomputing platforms. Results compare performance between the vector-based Cray X1, Earth Simulator, and newly-released NEC SX-8, with the commodity-based superscalar platforms of the IBM Power3, IntelItanium2, and AMD Opteron. Overall results show that the SX-8 attains unprecedented aggregate performance across our evaluated applications.
Lattice Boltzmann Simulation of Shale Gas Transport in Organic Nano-Pores
Zhang, Xiaoling; Xiao, Lizhi; Shan, Xiaowen; Guo, Long
2014-01-01
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale. PMID:24784022
Lattice-Boltzmann simulation of inertial particle-laden flow around an obstacle
NASA Astrophysics Data System (ADS)
Haddadi, Hamed; Shojaei-Zadeh, Shahab; Morris, Jeffrey F.
2016-06-01
The lattice-Boltzmann method is used to compute the flow of a particle suspension of dilute volume fraction ϕ ≤0.08 around obstacles. The work focuses on the interaction of particles with the obstacle and the flow behavior in and around the recirculating wake behind the obstacle. Motivated by microfluidic experiments of dilute suspension flow over obstacles of circular, square, and other shapes showing depletion of particles in the wake behind the obstacle, we focus on the entry and exit from the wake for isolated particles, small groups of particles, and a suspension of many particles. All work is at conditions well below the Reynolds number for the transition to unsteady flow and vortex shedding. The dynamics of an isolated particle inside the recirculating wake flow exhibits motion toward a limit cycle near the outer boundary of the wake. By increasing particle density above the fluid and increasing the size of the particle, we determine the upper limits of these variables yielding a limit cycle trajectory. Hydrodynamic interaction between particles in a many-particle suspension is shown to lead to exchange of particles between the wake zone and free stream.
Chatterjee, Dipankar; Amiroudine, Sakir
2011-02-01
A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative. PMID:21053082
Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis.
Sun, Chenghai; Munn, Lance L
2005-03-01
Historically, predicting macroscopic blood flow characteristics such as viscosity has been an empirical process due to the difficulty in rigorously including the particulate nature of blood in a mathematical representation of blood rheology. Using a two-dimensional lattice Boltzmann approach, we have simulated the flow of red blood cells in a blood vessel to estimate flow resistance at various hematocrits and vessel diameters. By including white blood cells (WBCs) in the flow, we also calculate the increase in resistance due to white cell rolling and adhesion. The model considers the blood as a suspension of particles in plasma, accounting for cell-cell and cell-wall interactions to predict macroscopic blood rheology. The model is able to reproduce the Fahraeus-Lindqvist effect, i.e., the increase in relative apparent viscosity as tube size increases, and the Fahraeus effect, i.e., tube hematocrit is lower than discharge hematocrit. In addition, the model allows direct assessment of the effect of WBCs on blood flow in the microvasculature, reproducing the dramatic increases in flow resistance as WBCs enter short capillary segments. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition. PMID:15613630
NASA Astrophysics Data System (ADS)
Gupta, A.; Sbragaglia, M.; Scagliarini, A.
2015-06-01
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behavior of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" interaction model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical results are compared with the predictions of various theoretical models. The proposed numerical simulations explore problems where the capabilities of LBM were never quantified before.
Lattice Boltzmann simulation of gas-solid adsorption processes at pore scale level
NASA Astrophysics Data System (ADS)
Zhou, L.; Qu, Z. G.; Chen, L.; Tao, W. Q.
2015-11-01
A two-dimensional lattice Boltzmann (LB) approach was established to implement kinetic concentration boundary conditions in interfacial mass-transfer processes and to simulate the adsorption process in porous media at pore scale and mesoscopic levels. A general treatment was applied to conduct three types of concentration boundary conditions effectively and accurately. Applicability for adsorption was verified by two benchmark examples, which were representative of the interparticle mass transport and intraparticle mass transport in the adsorption system, respectively. The gas-solid adsorption process in reconstructed porous media at the pore scale level was numerically investigated. Mass-transfer processes of the adsorption reaction were simulated by executing Langmuir adsorption kinetics on surfaces of adsorbent particles. Meanwhile, the homogeneous solid diffusion model (HSDM) was used for mass transport in interior particles. The transient adsorbed amount was obtained in detail, and the impact of flow condition, porosity, and adsorbent particle size on the entire dynamic adsorption performance was investigated. The time needed to approach steady state decreased with increased fluid velocity. Transient adsorption capability and time consumption to equilibrium were nearly independent of porosity, whereas increasing pore size led to a moderating adsorption rate and more time was consumed to approach the saturation adsorption. Benefiting from the advantages of the LB method, both bulk and intraparticle mass transfer performances during adsorption can be obtained using the present pore scale approach. Thus, interparticle mass transfer and intraparticle mass transfer are the two primary segments, and intraparticle diffusion has the dominant role.
Lattice Boltzmann simulation of rising bubble dynamics using an effective buoyancy method
NASA Astrophysics Data System (ADS)
Ngachin, Merlin; Galdamez, Rinaldo G.; Gokaltun, Seckin; Sukop, Michael C.
2015-08-01
This study describes the behavior of bubbles rising under gravity using the Shan and Chen-type multicomponent multiphase lattice Boltzmann method (LBM) [X. Shan and H. Chen, Phys. Rev. E47, 1815 (1993)]. Two-dimensional (2D) single bubble motions were simulated, considering the buoyancy effect for which the topology of the bubble was characterized by the nondimensional Eötvös (Eo), and Morton (M) numbers. In this study, a new approach based on the "effective buoyancy" was adopted and proven to be consistent with the expected bubble shape deformation. This approach expands the range of effective density differences between the bubble and the liquid that can be simulated. Based on the balance of forces acting on the bubble, it can deform from spherical to ellipsoidal shape with skirts appearing at high Eo number. A benchmark computational case for qualitative and quantitative validation was performed using COMSOL Multiphysics based on the level set method. Simulations were conducted for 1 ≤ Eo ≤ 100 and 3 × 10-6 ≤ M ≤ 2.73 × 10-3. Interfacial tension was checked through simulations without gravity, where Laplace's law was satisfied. Finally, quantitative analyses based on the terminal rise velocity and the degree of circularity was performed for various Eo and M values. Our results were compared with both the theoretical shape regimes given in literature and available simulation results.
NASA Astrophysics Data System (ADS)
Zarghami, Ahad; Looije, Niels; Van den Akker, Harry
2015-08-01
The pseudopotential lattice Boltzmann model (PP-LBM) is a very popular model for simulating multiphase systems. In this model, phase separation occurs via a short-range attraction between different phases when the interaction potential term is properly chosen. Therefore, the potential term is expected to play a significant role in the model and to affect the accuracy and the stability of the computations. The original PP-LBM suffers from some drawbacks such as being capable of dealing with low density ratios only, thermodynamic inconsistency, and spurious velocities. In this paper, we aim to analyze the PP-LBM with the view to simulate single-component (non-)isothermal multiphase systems at large density ratios and in spite of the presence of spurious velocities. For this purpose, the performance of two popular potential terms and of various implementation schemes for these potential terms is examined. Furthermore, the effects of different parameters (i.e., equation of state, viscosity, etc.) on the simulations are evaluated, and, finally, recommendations for a proper simulation of (non-)isothermal multiphase systems are presented.
Investigation of turbulence modulation in particle-laden flows using the lattice Boltzmann method.
NASA Astrophysics Data System (ADS)
Peng, Cheng; Geneva, Nicholas; Min, Haoda; Wang, Lian-Ping
2015-11-01
Turbulent modulation by finite-size solid particles has been studied experimentally and numerically in the past several decades. Previous studies have revealed that resolving the interfaces between particle surfaces and fluid is crucial to properly include finite-size effects on local fluid turbulence. Finite-size particles also produce pseudo-turbulence that may not decay locally, leading to a stronger nonlinear dependence of the level of turbulence modulation on the particle volume fraction. In this study we apply the lattice Boltzmann method (LBM) to perform interface-resolved simulations of turbulent particle-laden flow, focusing on local turbulence dynamics at the scale of particle size. We will discuss the accuracy of this mesoscopic approach when compared to other macroscopic methods. We consider both fully developed homogeneous isotropic (HI) turbulent flows and turbulent channel flows laden with finite-size particles. The particle volume fraction is around 10% and the particle-to-fluid density ratio is of the order of one. Conditional statistics as a function of distance from the moving particle surfaces are studied in detail, and are used to help interpret global turbulence modulation by particles. Grid convergence of these conditional statistics will be discussed.
Development of magneto-thermal lattice Boltzmann heat and fluid flow simulation
NASA Astrophysics Data System (ADS)
Kaneda, Masayuki; Kano, Hironori; Suga, Kazuhiko
2015-09-01
In this study, magneto-thermal lattice Boltzmann model is developed and heat transfer enhancement is investigated for a porous media heat exchanger. First, two models of thermal LBM are discussed in terms of its precision and applicability to magneto-thermal LBM including tolerance range of computational parameter. The implemented magneto-thermal LBM is then validated by convection in a cubic enclosure comparing with finite difference computation. The incompressibility limit of magneto-thermal LBM is additionally discussed. Finally, the effect of magnetic field on a flow through heated porous media is numerically investigated. It is found that, the magneto-thermal force is effective at the stagnant region inside the porous media to enhance the heat transfer. In a macroscopic view, the heat transfer enhancement is found in overall region. The effect becomes remarkable at low Reynolds number flow. Since its effect is aligned on a curve of Nusselt-Reynolds relation, the magnetic effect obviously found to assist the main flow.
A lattice Boltzmann model for substrates with regularly structured surface roughness
NASA Astrophysics Data System (ADS)
Yagub, A.; Farhat, H.; Kondaraju, S.; Singh, T.
2015-11-01
Superhydrophobic surface characteristics are important in many industrial applications, ranging from the textile to the military. It was observed that surfaces fabricated with nano/micro roughness can manipulate the droplet contact angle, thus providing an opportunity to control the droplet wetting characteristics. The Shan and Chen (SC) lattice Boltzmann model (LBM) is a good numerical tool, which holds strong potentials to qualify for simulating droplets wettability. This is due to its realistic nature of droplet contact angle (CA) prediction on flat smooth surfaces. But SC-LBM was not able to replicate the CA on rough surfaces because it lacks a real representation of the physics at work under these conditions. By using a correction factor to influence the interfacial tension within the asperities, the physical forces acting on the droplet at its contact lines were mimicked. This approach allowed the model to replicate some experimentally confirmed Wenzel and Cassie wetting cases. Regular roughness structures with different spacing were used to validate the study using the classical Wenzel and Cassie equations. The present work highlights the strength and weakness of the SC model and attempts to qualitatively conform it to the fundamental physics, which causes a change in the droplet apparent contact angle, when placed on nano/micro structured surfaces.
O'Connor, Joseph; Day, Philip; Mandal, Parthasarathi; Revell, Alistair
2016-05-16
Patient-specific simulations, efficient parametric analyses, and the study of complex processes that are otherwise experimentally intractable are facilitated through the use of Computational Fluid Dynamics (CFD) to study biological flows. This review discusses various CFD methodologies that have been applied across different biological scales, from cell to organ level. Through this discussion the lattice Boltzmann method (LBM) is highlighted as an emerging technique capable of efficiently simulating fluid problems across the midrange of scales; providing a practical analytical tool compared to methods more attuned to the extremities of scale. Furthermore, the merits of the LBM are highlighted through examples of previous applications and suggestions for future research are made. The review focusses on applications in the midrange bracket, such as cell-cell interactions, the microcirculation, and microfluidic devices; wherein the inherent mesoscale nature of the LBM renders it well suited to the incorporation of fluid-structure interaction effects, molecular/particle interactions and interfacial dynamics. The review demonstrates that the LBM has the potential to become a valuable tool across a range of emerging areas in bio-CFD, such as understanding and predicting disease, designing lab-on-a-chip devices, and elucidating complex biological processes. PMID:27068565
Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation.
Ren, Feng; Song, Baowei; Sukop, Michael C; Hu, Haibao
2016-08-01
The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015)10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014)10.1103/PhysRevE.89.053320]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling. PMID:27627416
A new lattice Boltzmann model for interface reactions between immiscible fluids
NASA Astrophysics Data System (ADS)
Di Palma, Paolo Roberto; Huber, Christian; Viotti, Paolo
2015-08-01
In this paper, we describe a lattice Boltzmann model to simulate chemical reactions taking place at the interface between two immiscible fluids. The phase-field approach is used to identify the interface and its orientation, the concentration of reactant at the interface is then calculated iteratively to impose the correct reactive flux condition. The main advantages of the model is that interfaces are considered part of the bulk dynamics with the corrective reactive flux introduced as a source/sink term in the collision step, and, as a consequence, the model's implementation and performance is independent of the interface geometry and orientation. Results obtained with the proposed model are compared to analytical solution for three different benchmark tests (stationary flat boundary, moving flat boundary and dissolving droplet). We find an excellent agreement between analytical and numerical solutions in all cases. Finally, we present a simulation coupling the Shan Chen multiphase model and the interface reactive model to simulate the dissolution of a collection of immiscible droplets with different sizes rising by buoyancy in a stagnant fluid.
Simulation of binary droplet collisions with the entropic lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Mazloomi Moqaddam, Ali; Chikatamarla, Shyam S.; Karlin, Ilya V.
2016-02-01
The recently introduced entropic lattice Boltzmann method (ELBM) for multiphase flows is extended here to simulation of droplet collisions. Thermodynamically consistent, non-linearly stable ELBM together with a novel polynomial equation of state is proposed for simulation large Weber and Reynolds number collisions of two droplets. Extensive numerical investigations show that ELBM is capable of accurately capturing the dynamics and complexity of droplet collision. Different types of the collision outcomes such as coalescence, reflexive separation, and stretching separation are identified. Partition of the parameter plane is compared to the experiments and excellent agreement is observed. Moreover, the evolution of the shape of a stable lamella film is quantitatively compared with experimental results. The end pinching and the capillary-wave instability are shown to be the main mechanisms behind formation of satellite droplets for near head-on and off-center collisions with high impact parameter, respectively. It is shown that the number of satellite drops increases with increasing Weber number, as predicted by experiments. Also, it is demonstrated that the rotational motion due to angular momentum and elongation of the merged droplet play essential roles in formation of satellite droplets in off-center collisions with an intermediate impact parameter.
Fluid flow and mass transfer over circular strands using the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Hossain, Md. Shakhawath; Chen, X. B.; Bergstrom, D. J.
2015-10-01
Knowledge of the fluid flow and mass transfer over circular strands is fundamental to the cell culture of tissue scaffolds in bio-reactors. This paper presents a study on the simulation of fluid flow and mass transfer over the circular strands of a tissue scaffold by using the multiple relaxation time lattice Boltzmann method for the low Reynolds number regime, with Re D = 0.01 and 0.1, respectively. The mass transfer problem approximates the transport of a scalar nutrient from the bulk fluid to the strand surface, such as is encountered in the flow through tissue scaffolds placed in bio-reactors. The circular geometry of the scaffold strand is treated and implemented by means of the interpolated bounce-back boundary condition formulation. Our simulation illustrates that the flow accelerates around the strand, resulting in the maximum shear stress at the shoulder of the strand and that diffusion mass transfer plays the dominant role in the scalar transport. The local Sherwood number varies significantly over the surface of the strand, with a peak value located on the upstream surface. Increasing the Schmidt number of the scalar and decreasing the blockage ratio results in higher mass transfer rates on the surface of the stand. Overall, the simulation results provide one with the insight into the fluid flow and mass transfer over the circular strands of a tissue scaffold in a bio-reactor, which would be impractical to obtain by experiments.
Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect.
Chen, Li; Fang, Wenzhen; Kang, Qinjun; De'Haven Hyman, Jeffrey; Viswanathan, Hari S; Tao, Wen-Quan
2015-03-01
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix. PMID:25871199
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247
Optimization of a Lattice Boltzmann Computation on State-of-the-Art Multicore Platforms
Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine
2009-04-10
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Xeon E5345 (Clovertown), AMD Opteron 2214 (Santa Rosa), AMD Opteron 2356 (Barcelona), Sun T5140 T2+ (Victoria Falls), as well as a QS20 IBM Cell Blade. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 15x improvement compared with the original code at a given concurrency. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
Lattice Boltzmann Simulation of Healthy and Defective Red Blood Cell Settling in Blood Plasma.
Hashemi, Z; Rahnama, M; Jafari, S
2016-05-01
In this paper, an attempt has been made to study sedimentation of a red blood cell (RBC) in a plasma-filled tube numerically. Such behaviors are studied for a healthy and a defective cell which might be created due to human diseases, such as diabetes, sickle-cell anemia, and hereditary spherocytosis. Flow-induced deformation of RBC is obtained using finite-element method (FEM), while flow and fluid-membrane interaction are handled using lattice Boltzmann (LB) and immersed boundary methods (IBMs), respectively. The effects of RBC properties as well as its geometry and orientation on its sedimentation rate are investigated and discussed. The results show that decreasing frontal area of an RBC and/or increasing tube diameter results in a faster settling. Comparison of healthy and diabetic cells reveals that less cell deformability leads to slower settling. The simulation results show that the sicklelike and spherelike RBCs have lower settling velocity as compared with a biconcave discoid cell. PMID:26926169
Towards mico-ThFFF for polymer analysis: Lattice-Boltzmann based simulations
NASA Astrophysics Data System (ADS)
Antonelli, Michael; Kreft Pearce, Jennifer
2014-11-01
Thermophoresis describes a behavior, observed at micro-scales, in which particles migrate due to a temperature gradient. The purpose of this project is to study the parameters that have the greatest effect on thermophoresis and to use these properties to design a device for separating biological macromolecules using extremely small samples. A Lattice-Boltzmann based computer simulation of a microfluidic cell was used to determine the conditions under which DNA molecules, in a buffered salt solution, will exhibit this phenomenon. The simulation monitored particle positions within the cell, beginning from random initial conditions. Particle-solvent and particle-particle interactions were examined. Particle-particle interactions were modeled using the Lennard-Jones potential. By modifying the distance at which potential is minimized as well as the magnitude of the potential, conditions that increase the response of the molecule to the temperature gradient were observed. Once satisfactory conditions had been determined, separation of particles in a theoretical microfluidic device was simulated. The periodic boundary conditions were changed and a more dynamic channel was modeled. Unidirectional flow fields as well as particles with differing thermophoretic properties were simulated in the micro-channel and their concentrations across the channel measured.
NASA Astrophysics Data System (ADS)
Alapati, Suresh; Che, Woo Seong; Mannoor, Madhusoodanan; Suh, Yong Kweon
2016-06-01
In this paper, we present the results obtained from the simulation of particle motion induced by the fluid flow driven by an array of beating artificial cilia inside a micro-channel. A worm-like-chain model is used to simulate the elastic cilia, and the lattice Boltzmann equation is used to compute the fluid flow. We employ a harmonic force at the extreme tip of each cilium to actuate it. Our simulation methods are first validated by applying them to the motion of a single cilium and a freely falling sphere. After validation, we simulate the fluid flow generated by an array of beating cilia and find that a maximum flow rate is achieved at an optimum sperm number. Next, we simulate the motion of a neutrally buoyant spherical particle at this optimum sperm number by tracking the particle motion with a smoothed profile method. We address the effect of the following parameters on the particle velocity: the gap between cilia and particle, the particle size, the cilia density, and the presence of an array of intermediate particles.
Hekmat, Mohamad Hamed; Mirzaei, Masoud
2015-01-01
In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced. PMID:25679735
NASA Astrophysics Data System (ADS)
Goryachev, Maxim; Tobar, Michael E.
2015-02-01
A new electromagnetic cavity structure, a lattice of 3D cavities consisting of an array of posts and gaps is presented. The individual cavity elements are based on the cylindrical re-entrant (or Klystron) cavity. We show that these cavities can also be thought of as 3D split-ring resonators, which is confirmed by applying symmetry transformations, each of which is an electromagnetic resonator with spatially separated magnetic and electric field. The characteristics of the cavity is used to mimic phonon behaviour of a one-dimensional (1D) chain of atoms. It is demonstrated how magnetic field coupling can lead to phonon-like dispersion curves with acoustical and optical branches. The system is able to reproduce a number of effects typical to 1D lattices exhibiting acoustic vibration, such as band gaps, phonon trapping, and effects of impurities. In addition, quasicrystal emulations predict the results expected from this class of ordered structures. The system is easily scalable to simulate two-dimensional and 3D lattices and shows a new way to engineer arrays of coupled microwave resonators with a variety of possible applications to hybrid quantum systems proposed.
Sukop, Michael C.; Huang, Haibo; Alvarez, Pedro F.; Variano, Evan A.; Cunningham, Kevin J.
2013-01-01
Lattice Boltzmann flow simulations provide a physics-based means of estimating intrinsic permeability from pore structure and accounting for inertial flow that leads to departures from Darcy's law. Simulations were used to compute intrinsic permeability where standard measurement methods may fail and to provide better understanding of departures from Darcy's law under field conditions. Simulations also investigated resolution issues. Computed tomography (CT) images were acquired at 0.8 mm interscan spacing for seven samples characterized by centimeter-scale biogenic vuggy macroporosity from the extremely transmissive sole-source carbonate karst Biscayne aquifer in southeastern Florida. Samples were as large as 0.3 m in length; 7–9 cm-scale-length subsamples were used for lattice Boltzmann computations. Macroporosity of the subsamples was as high as 81%. Matrix porosity was ignored in the simulations. Non-Darcy behavior led to a twofold reduction in apparent hydraulic conductivity as an applied hydraulic gradient increased to levels observed at regional scale within the Biscayne aquifer; larger reductions are expected under higher gradients near wells and canals. Thus, inertial flows and departures from Darcy's law may occur under field conditions. Changes in apparent hydraulic conductivity with changes in head gradient computed with the lattice Boltzmann model closely fit the Darcy-Forchheimer equation allowing estimation of the Forchheimer parameter. CT-scan resolution appeared adequate to capture intrinsic permeability; however, departures from Darcy behavior were less detectable as resolution coarsened.
Detecting the Chern number of topological Weyl semimetals in 3D optical lattices
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Cao, Shuai
2016-06-01
We propose a realistic scheme to directly probe the Chern number of topological Weyl semimetals in optical lattices. The Weyl semimetal states can be realized with ultracold fermionic atoms trapped in three-dimensional optical lattices, and are topologically characterized by k z -dependent Chern number, where k z is the out-of-plane quasimomentum. We demonstrate with numerical simulations that this characteristic topological invariant can be extracted from the shift of the hybrid Wannier center in the optical lattice, based on the particle pumping approach. Through in situ measurement of atomic density, the topological properties of the Weyl semimetal states are then directly revealed.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
Water Management In PEM Fuel Cell - A Lattice-Boltzmann Modeling Approach
Mukherjee, Shiladitya; Cole, James Vernon; Jain, Kunal; Gidwani, Ashok
2009-06-01
In Proton Exchange Membrane Fuel Cells (PEMFCs), water management and the effective transport of water through the gas-diffusion-layer (GDL) are key issues for improved performance at high power density and for durability during freeze-thaw cycles. The diffusion layer is a thin (~150-350{micro}m), porous material typically composed of a web of carbon fibers and particles, and is usually coated with hydrophobic Teflon to remove the excess water through capillary action. In-situ diagnostics of water movement and gas-reactant transport through this thin opaque substrate is challenging. Numerical analyses are typically based on simplified assumptions, such as Darcy's Law and Leverett functions for the capillary pressure. The objective of this work is to develop a high fidelity CFD modeling and analysis tool to capture the details of multiphase transport through the porous GDL. The tool can be utilized to evaluate GDL material design concepts and optimize systems based on the interactions between cell design, materials, and operating conditions. The flow modeling is based on the Lattice Boltzmann Method (LBM). LBM is a powerful modeling tool to simulate multiphase flows. Its strength is in its kinetic theory based foundation, which provides a fundamental basis for incorporating intermolecular forces that lead to liquid-gas phase separation and capillary effects without resorting to expensive or ad-hoc interface reconstruction schemes. At the heart of the solution algorithm is a discrete form of the well-known Boltzmann Transport Equation (BTE) for molecular distribution, tailored to recover the continuum Navier-Stokes flow. The solution advances by a streaming and collision type algorithm, mimicking actual molecular physics, which makes it suitable for porous media involving complex boundaries. We developed a numerical scheme to reconstruct various porous GDL microstructures including Teflon loading. Single and multiphase LBM models are implemented to compute
2D and 3D Anilato-Based Heterometallic M(I)M(III) Lattices: The Missing Link.
Benmansour, Samia; Vallés-García, Cristina; Gómez-Claramunt, Patricia; Mínguez Espallargas, Guillermo; Gómez-García, Carlos J
2015-06-01
The similar bis-bidentate coordination mode of oxalato and anilato-based ligands is exploited here to create the first examples of 2D and 3D heterometallic lattices based on anilato ligands combining M(I) and a M(III) ions, phases already observed with oxalato but unknown with anilato-type ligands. These lattices are prepared with alkaline metal ions and magnetic chiral tris(anilato)metalate molecular building blocks: [M(III)(C6O4X2)3](3-) (M(III) = Fe and Cr; X = Cl and Br; (C6O4X2)(2-) = dianion of the 3,6-disubstituted derivatives of 2,5-dihydroxy-1,4-benzoquinone, H4C6O4). The new compounds include two very similar 2D lattices formulated as (PBu3Me)2[NaCr(C6O4Br2)3] (1) and (PPh3Et)2[KFe(C6O4Cl2)3](dmf)2 (2), both presenting hexagonal [M(I)M(III)(C6O4X2)3](2-) honeycomb layers with (PBu3Me)(+) in 1 or (PPh3Et)(+) and dmf in 2 inserted between them. Minor modifications in the synthetic conditions yield the novel 3D lattice (NEt3Me)[Na(dmf)][NaFe(C6O4Cl2)3] (3), in which hexagonal layers analogous to 1 and 2 are interconnected through Na(+) cations, and (NBu3Me)2[NaCr(C6O4Br2)3] (4), the first heterometallic 3D lattice based on anilato ligands. This compound presents two interlocked chiral 3D (10,3) lattices with opposite chiralities. Attempts to prepare 4 in larger quantities result in the 2D polymorph of compound 4 (4'). Magnetic properties of compounds 1, 3, and 4' are reported, and in all cases we observe, as expected, paramagnetic behaviors that can be satisfactorily reproduced with simple monomer models including a zero field splitting (ZFS) of the corresponding S = 3/2 for Cr(III) in 1 and 4' or S = 5/2 for Fe(III) in 3. PMID:25965415
Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M
2013-10-01
In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. PMID:23859813
Bai, Liping; Baker, Don R.; Hill, Reghan J.
2010-09-17
The permeabilities of vesicular Stromboli basaltic glasses were determined using lattice Boltzmann (LB) simulations and laboratory measurements. Lattice Boltzmann simulations were performed to simulate flow through vesicular Stromboli basaltic glasses with porosities, {phi}, from 5% to 92%. The simulations and measurements provide a power law Darcian permeability-porosity relationship k(Phi) = c ({phi}){sup 5} with c = 2.35 x 10{sup -20} from LB simulations and 5.33 x 10{sup -21} from measurements, where k is in m{sup 2}. These permeabilities of vesiculated basalts are about 1 to 2 orders of magnitude higher than in rhyolitic and dacitic volcanic rocks with the same porosity; this difference is attributed to a higher bubble interconnectivity and larger bubble apertures in our basaltic samples. The Darcian flow permeability k{sub 1} (m{sup 2}) and non-Darcian flow permeability k{sub 2} (m) are highly dependent on bubble size, D, and porosity with k{sub 1} = 7.66 x 10{sup -17}[D{sup 2{phi}3}/(1 - {phi}){sup 2}] and k{sub 2} = 2.78 x 10{sup -9}[D{phi}{sup 3}/(1 - {phi})]. Samples with power law bubble size distributions can produce higher permeabilities than samples with exponential bubble size distributions. The Darcian and non-Darcian flow regimes are delineated, demonstrating that the Darcian flow occurs at the Forchheimer number, Fo, below 0.2-1, and the transitional flow (Forchheimer flow) occurs in the Forchheimer number range 1 to 10. The correlations between friction factor, f{sub k}, and Fo are constrained by the permeability measurements, and are in good agreement with simulations: f{sub k} = (1.11 {+-} 0.17) + [(0.66 {+-} 0.39)/Fo] (measurements) and f{sub k} = (0.59 {+-} 0.49) + [(1.0 {+-} 0.01)/Fo] (LB simulations). Our results show that f{sub k} depends on k{sub 2}, pore size, and pore geometry at small Fo and tends to be a constant at large Fo. The f{sub k} - Fo correlations imply a gradual transition from Darcian to non-Darcian flow, rather than an
Lattice Boltzmann simulation of water isotope fractionation during ice crystal growth in clouds
NASA Astrophysics Data System (ADS)
Lu, Guoping; DePaolo, Donald J.
2016-05-01
We describe a lattice Boltzmann (LB) method for simulating water isotope fractionation during diffusion-limited ice crystal growth by vapor deposition from water-oversaturated air. These conditions apply to the growth of snow crystals in clouds where the vapor composition is controlled by the presence of both ice crystals and water droplets. Modeling of water condensation with the LB method has the advantage of allowing concentration fields to evolve based on local conditions so that the controls on grain shapes of the condensed phase can be studied simultaneously with the controls on isotopic composition and growth rate. Water isotope fractionation during snow crystal growth involves kinetic effects due to diffusion of water vapor in air, which requires careful consideration of the boundary conditions at the ice-vapor interface. The boundary condition is relatively simple for water isotopes because the molecular exchange rate for water at the interface is large compared to the crystal growth rate. Our results for the bulk crystal isotopic composition are consistent with simpler models using analytical solutions for radial geometry. However, the model results are sufficiently different for oxygen isotopes that they could affect the interpretation of D-excess values of snow and ice. The extent of vapor oversaturation plays a major role in determining the water isotope fractionation as well as the degree of dendritic growth. Departures from isotopic equilibrium increase at colder temperatures as diffusivity decreases. Dendritic crystals are isotopically heterogeneous. Isotopic variations within individual snow crystals could yield information on the microphysics of ice condensation as well as on the accommodation or sticking coefficient of water associated with vapor deposition. Our results are ultimately a first step in implementing LB models for kinetically controlled condensation or precipitation reactions, but needs to be extended also to cases where the
A Lattice Boltzmann model for simulating water flow at pore scale in unsaturated soils
NASA Astrophysics Data System (ADS)
Zhang, Xiaoxian; Crawford, John W.; Young, Iain M.
2016-07-01
The Lattice Boltzmann (LB) method is an established prominent model for simulating water flow at pore scale in saturated porous media. However, its application in unsaturated soil is less satisfactory because of the difficulties associated with most two-phase LB models in simulating immiscible fluids, such as water and air, which have contrasting densities and viscosities. While progress has been made in developing LB models for fluids with high density ratio, they are still prone to numerical instability and cannot accurately describe the interfacial friction on water-air interface in unsaturated media. Considering that one important application of the LB model in porous materials is to calculate their hydraulic properties when flow is at steady state, we develop a simple LB model to simulate steady water flow at pore scale in unsaturated soils. The method consists of two steps. The first one is to determine water distribution within the soil structure using a morphological model; once the water distribution is known, its interfaces with air are fixed. The second step is to use a single-phase LB model to simulate water flow by treating the water-air interfaces as free-flow boundaries where the shear resistance of air to water flow is assumed to be negligible. We propose a method to solve such free-flow boundaries, and validate the model against analytical solutions of flows of water film over non-slip walls in both two and three dimensions. We then apply the model to calculate water retention and hydraulic properties of a medium acquired using X-ray computed tomography at resolution of 6 μm. The model is quasi-static, similar to the porous network model, but is an improvement as it directly simulates water flow in the pore geometries acquired by tomography without making any further simplifications.
Anupindi, Kameswararao; Lai, Weichen; Frankel, Steven
2014-01-01
In the present work, lattice Boltzmann method (LBM) is applied for simulating flow in a three-dimensional lid driven cubic and deep cavities. The developed code is first validated by simulating flow in a cubic lid driven cavity at 1000 and 12000 Reynolds numbers following which we study the effect of cavity depth on the steady-oscillatory transition Reynolds number in cavities with depth aspect ratio equal to 1, 2 and 3. Turbulence modeling is performed through large eddy simulation (LES) using the classical Smagorinsky sub-grid scale model to arrive at an optimum mesh size for all the simulations. The simulation results indicate that the first Hopf bifurcation Reynolds number correlates negatively with the cavity depth which is consistent with the observations from two-dimensional deep cavity flow data available in the literature. Cubic cavity displays a steady flow field up to a Reynolds number of 2100, a delayed anti-symmetry breaking oscillatory field at a Reynolds number of 2300, which further gets restored to a symmetry preserving oscillatory flow field at 2350. Deep cavities on the other hand only attain an anti-symmetry breaking flow field from a steady flow field upon increase of the Reynolds number in the range explored. As the present work involved performing a set of time-dependent calculations for several Reynolds numbers and cavity depths, the parallel performance of the code is evaluated a priori by running the code on up to 4096 cores. The computational time required for these runs shows a close to linear speed up over a wide range of processor counts depending on the problem size, which establishes the feasibility of performing a thorough search process such as the one presently undertaken. PMID:24587561
Anupindi, Kameswararao; Lai, Weichen; Frankel, Steven
2014-03-20
In the present work, lattice Boltzmann method (LBM) is applied for simulating flow in a three-dimensional lid driven cubic and deep cavities. The developed code is first validated by simulating flow in a cubic lid driven cavity at 1000 and 12000 Reynolds numbers following which we study the effect of cavity depth on the steady-oscillatory transition Reynolds number in cavities with depth aspect ratio equal to 1, 2 and 3. Turbulence modeling is performed through large eddy simulation (LES) using the classical Smagorinsky sub-grid scale model to arrive at an optimum mesh size for all the simulations. The simulation results indicate that the first Hopf bifurcation Reynolds number correlates negatively with the cavity depth which is consistent with the observations from two-dimensional deep cavity flow data available in the literature. Cubic cavity displays a steady flow field up to a Reynolds number of 2100, a delayed anti-symmetry breaking oscillatory field at a Reynolds number of 2300, which further gets restored to a symmetry preserving oscillatory flow field at 2350. Deep cavities on the other hand only attain an anti-symmetry breaking flow field from a steady flow field upon increase of the Reynolds number in the range explored. As the present work involved performing a set of time-dependent calculations for several Reynolds numbers and cavity depths, the parallel performance of the code is evaluated a priori by running the code on up to 4096 cores. The computational time required for these runs shows a close to linear speed up over a wide range of processor counts depending on the problem size, which establishes the feasibility of performing a thorough search process such as the one presently undertaken. PMID:24587561
Fast discontinuous Galerkin lattice-Boltzmann simulations on GPUs via maximal kernel fusion
NASA Astrophysics Data System (ADS)
Mazzeo, Marco D.
2013-03-01
A GPU implementation of the discontinuous Galerkin lattice-Boltzmann method with square spectral elements, and highly optimised for speed and precision of calculations is presented. An extensive analysis of the numerous variants of the fluid solver unveils that best performance is obtained by maximising CUDA kernel fusion and by arranging the resulting kernel tasks so as to trigger memory coherent and scattered loads in a specific manner, albeit at the cost of introducing cross-thread load unbalancing. Surprisingly, any attempt to vanish this, to maximise thread occupancy and to adopt conventional work tiling or distinct custom kernels highly tuned via ad hoc data and computation layouts invariably deteriorate performance. As such, this work sheds light into the possibility to hide fetch latencies of workloads involving heterogeneous loads in a way that is more effective than what is achieved with frequently suggested techniques. When simulating the lid-driven cavity on a NVIDIA GeForce GTX 480 via a 5-stage 4th-order Runge-Kutta (RK) scheme, the first four digits of the obtained centreline velocity values, or more, converge to those of the state-of-the-art literature data at a simulation speed of 7.0G primitive variable updates per second during the collision stage and 4.4G ones during each RK step of the advection by employing double-precision arithmetic (DPA) and a computational grid of 642 4×4-point elements only. The new programming engine leads to about 2× performance w.r.t. the best programming guidelines in the field. The new fluid solver on the above GPU is also 20-30 times faster than a highly optimised version running on a single core of a Intel Xeon X5650 2.66 GHz.
Shape changes of bioprinted tissue constructs simulated by the Lattice Boltzmann method.
Cristea, Artur; Neagu, Adrian
2016-03-01
Tissue engineers seek to build living tissue constructs for replacing or repairing damaged tissues. Computational methods foster tissue engineering by pointing out dominant mechanisms involved in shaping multicellular systems. Here we apply the Lattice Boltzmann (LB) method to study the fusion of multicellular constructs. This process is of interest in bioprinting, in which multicellular spheroids or cylinders are embedded in a supportive hydrogel by a computer-controlled device. We simulated post-printing rearrangements of cells, aiming to predict the shape and stability of certain printed structures. To this end, we developed a two-dimensional LB model of a multicellular system in a hydrogel. Our parallel computing code was implemented using the Portable Extensible Toolkit for Scientific Computation (PETSc). To validate the LB model, we simulated the fusion of multicellular cylinders in a contiguous, hexagonal arrangement. Our two-dimensional LB simulation describes the evolution of the transversal cross section of the construct built from three-dimensional multicellular cylinders whose length is much larger than their diameter. Fusion eventually gave rise to a tubular construct, in qualitative agreement with bioprinting experiments. Then we simulated the time course of a defect in a bioprinted tube. To address practical problems encountered in tissue engineering, we also simulated the evolution of a planar construct, as well as of a bulky, perfusable construct made of multicellular cylinders. The agreement with experiments indicates that our LB model captures certain essential features of morphogenesis, and, therefore, it may be used to test new working hypotheses faster and cheaper than in the laboratory. PMID:26803291
Chau, Jessica Furrer; Or, Dani
2006-11-01
The effect of drainage front morphology on gaseous diffusion through partially saturated porous media is analyzed using the lattice Boltzmann method (LBM). Flow regimes for immiscible displacement in porous media have been characterized as stable displacement, capillary fingering, and viscous fingering. The dominance of a flow regime is associated with the relative magnitudes of gravity, viscous, and capillary forces, quantifiable via the Bond number Bo, capillary number Ca, and their difference, Bo-Ca . Forced drainage from an initially saturated two-dimensional (2D) porous medium was simulated and the resulting flow patterns were analyzed and compared with theoretical predictions and experimental results. The LBM simulations reproduced expected flow morphologies for a range of drainage velocities and gravitational forces (i.e., a range of capillary and Bond numbers). Furthermore, measures of drainage front width as a function of the dimensionless difference Bo-Ca correspond well with scaling laws derived from percolation theory. Effects of flow morphology on residual fluid entrapment and gaseous diffusion were assessed by running LBM diffusion simulations through the partially saturated domain for a range of water contents. The effective diffusion coefficient as a function of water content was estimated for three regimes: stable drainage front, capillary fingering, and viscous fingering. Significant reductions in gaseous diffusion coefficient were found for viscous fingering relative to stable displacement, and to a lesser extent for capillary fingering, indicating that wetting phase distribution with a high degree of fingering in the 2D domain severely restricts connectivity of gas diffusion pathways through the medium. The study lends support for the use of LBM in design and management of fluids in porous media under variable gravity, and enhances the understanding of the role of dynamic fluid behavior on macroscopic transport properties of partially saturated
Potential of lattice Boltzmann to model droplets on chemically stripe-patterned substrates
NASA Astrophysics Data System (ADS)
Patrick Jansen, H.; Sotthewes, K.; Zandvliet, Harold J. W.; Kooij, E. Stefan
2016-01-01
Lattice Boltzmann modelling (LBM) has recently been applied to a range of different wetting situations. Here we demonstrate its potential in representing complex kinetic effects encountered in droplets on chemically stripe-patterned surfaces. An ultimate example of the power of LBM is provided by comparing simulations and experiments of impacting droplets with varying Weber numbers. Also, the shape evolution of droplets is discussed in relation to their final shape. The latter can then be compared to Surface Evolver (SE) results, since under the proper boundary conditions both approaches should yield the same configuration in a static state. During droplet growth in LBM simulations, achieved by increasing the density within the droplet, the contact line initially advances in the direction parallel to the stripes, therewith increasing its aspect ratio. Once the volume becomes too large the droplet starts wetting additional stripes, leading to a lower aspect ratio. The maximum aspect ratio is shown to be a function of the width ratio of the hydrophobic and hydrophilic stripes and also their absolute widths. In the limit of sufficiently large stripe widths the aspect ratio is solely dependent on the relative stripe widths. The maximum droplet aspect ratio in the LBM simulations is compared to SE simulations and results are shown to be in good agreement. Additionally, we also show the ability of LBM to investigate single stripe wetting, enabling determination of the maximum aspect ratio that can be achieved in the limit of negligible hydrophobic stripe width, under the constraint that the stripe widths are large enough such that they are not easily crossed.
Liu, Haihu; Zhang, Yonghao; Valocchi, Albert J.
2015-05-15
Injection of anthropogenic carbon dioxide (CO{sub 2}) into geological formations is a promising approach to reduce greenhouse gas emissions into the atmosphere. Predicting the amount of CO{sub 2} that can be captured and its long-term storage stability in subsurface requires a fundamental understanding of multiphase displacement phenomena at the pore scale. In this paper, the lattice Boltzmann method is employed to simulate the immiscible displacement of a wetting fluid by a non-wetting one in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We have identified three different displacement patterns, namely, stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number (Ca), viscosity ratio (M), and the media heterogeneity. The non-wetting fluid saturation (S{sub nw}) is found to increase nearly linearly with logCa for each constant M. Increasing M (viscosity ratio of non-wetting fluid to wetting fluid) or decreasing the media heterogeneity can enhance the stability of the displacement process, resulting in an increase in S{sub nw}. In either pore networks, the specific interfacial length is linearly proportional to S{sub nw} during drainage with equal proportionality constant for all cases excluding those revealing considerable viscous fingering. Our numerical results confirm the previous experimental finding that the steady state specific interfacial length exhibits a linear dependence on S{sub nw} for either favorable (M ≥ 1) or unfavorable (M < 1) displacement, and the slope is slightly higher for the unfavorable displacement.
NASA Astrophysics Data System (ADS)
Hosa, Aleksandra; Curtis, Andrew; Wood, Rachel
2016-08-01
A common way to simulate fluid flow in porous media is to use Lattice Boltzmann (LB) methods. Permeability predictions from such flow simulations are controlled by parameters whose settings must be calibrated in order to produce realistic modelling results. Herein we focus on the simplest and most commonly used implementation of the LB method: the single-relaxation-time BGK model. A key parameter in the BGK model is the relaxation time τ which controls flow velocity and has a substantial influence on the permeability calculation. Currently there is no rigorous scheme to calibrate its value for models of real media. We show that the standard method of calibration, by matching the flow profile of the analytic Hagen-Poiseuille pipe-flow model, results in a BGK-LB model that is unable to accurately predict permeability even in simple realistic porous media (herein, Fontainebleau sandstone). In order to reconcile the differences between predicted permeability and experimental data, we propose a method to calibrate τ using an enhanced Transitional Markov Chain Monte Carlo method, which is suitable for parallel computer architectures. We also propose a porosity-dependent τ calibration that provides an excellent fit to experimental data and which creates an empirical model that can be used to choose τ for new samples of known porosity. Our Bayesian framework thus provides robust predictions of permeability of realistic porous media, herein demonstrated on the BGK-LB model, and should therefore replace the standard pipe-flow based methods of calibration for more complex media. The calibration methodology can also be extended to more advanced LB methods.
Implicit-correction-based immersed boundary-lattice Boltzmann method with two relaxation times.
Seta, Takeshi; Rojas, Roberto; Hayashi, Kosuke; Tomiyama, Akio
2014-02-01
In the present paper, we verify the effectiveness of the two-relaxation-time (TRT) collision operator in reducing boundary slip computed by the immersed boundary-lattice Boltzmann method (IB-LBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The Chapman-Enskog expansion indicates that one relaxation time for the symmetric component is related to the kinematic viscosity. Rigorous analysis of the symmetric shear flows reveals that the relaxation time for the antisymmetric part controls the velocity gradient, the boundary velocity, and the boundary slip velocity computed by the IB-LBM. Simulation of the symmetric shear flows, the symmetric Poiseuille flows, and the cylindrical Couette flows indicates that the profiles of the numerical velocity calculated by the TRT collision operator under the IB-LBM framework exactly agree with those of the multirelaxation time (MRT). The TRT is as effective in removing the boundary slip as the MRT. We demonstrate analytically and numerically that the error of the boundary velocity is caused by the smoothing technique using the δ function used in the interpolation method. In the simulation of the flow past a circular cylinder, the IB-LBM based on the implicit correction method with the TRT succeeds in preventing the flow penetration through the solid surface as well as unphysical velocity distortion. The drag coefficient, the wake length, and the separation points calculated by the present IB-LBM agree well with previous studies at Re = 10, 20, and 40. PMID:25353605
Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization.
Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Li, Hua
2011-10-01
We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the
A Lattice Boltzmann Framework for the simulation of boiling hydrodynamics in BWRs.
Jain, P. K.; Tentner, A.; Uddin, R.
2008-01-01
Multi phase and multi component flows are ubiquitous in nature as well as in many man-made processes. A specific example is the Boiling Water Reactor (BWR) core, in which the coolant enters the core as liquid, undergoes a phase change as it traverses the core and exits as a high quality two-phase mixture. Two-phase flows in BWRs typically manifest a wide variety of geometrical patterns of the co-existing phases depending on the local system conditions. Modeling of such flows currently relies on empirical correlations (for example, in the simulation of bubble nucleation, bubble growth and coalescence, and inter-phase surface topology transitions) that hinder the accurate simulation of two-phase phenomena using Computational Fluid Dynamics (CFD) approaches. The Lattice Boltzmann Method (LBM) is in rapid development as a modeling tool to understand these macro-phenomena by coupling them with their underlying micro-dynamics. This paper presents a consistent LBM formulation for the simulation of a two-phase water-steam system. Results of initial model validation in a range of thermodynamic conditions typical for BWRs are also shown. The interface between the two coexisting phases is captured from the dynamics of the model itself, i.e., no interface tracking is needed. The model is based on the Peng-Robinson (P-R) non-ideal equation of state and can quantitatively approximate the phase-coexistence curve for water at different temperatures ranging from 125 to 325 oC. Consequently, coexisting phases with large density ratios (up to {approx}1000) may be simulated. Two-phase models in the 200-300 C temperature range are of significant importance to nuclear engineers since most BWRs operate under similar thermodynamic conditions. Simulation of bubbles and droplets in a gravity-free environment of the corresponding coexisting phase until steady state is reached satisfies Laplace law at different temperatures and thus, yield the surface tension of the fluid. Comparing the LBM
NASA Astrophysics Data System (ADS)
Favier, Julien; Revell, Alistair; Pinelli, Alfredo
2014-03-01
A numerical approach based on the Lattice Boltzmann and Immersed Boundary methods is proposed to tackle the problem of the interaction of moving and/or deformable slender solids with an incompressible fluid flow. The method makes use of a Cartesian uniform lattice that encompasses both the fluid and the solid domains. The deforming/moving elements are tracked through a series of Lagrangian markers that are embedded in the computational domain. Differently from classical projection methods applied to advance in time the incompressible Navier-Stokes equations, the baseline Lattice Boltzmann fluid solver is free from pressure corrector step, which is known to affect the accuracy of the boundary conditions. Also, in contrast to other immersed boundary methods proposed in the literature, the proposed algorithm does not require the introduction of any empirical parameter. In the case of rigid bodies, the position of the markers delimiting the surface of an object is updated by tracking both the position of the centre of mass of the object and its rotation using Newton's laws and the conservation of angular momentum. The dynamics of a flexible slender structure is determined as a function of the forces exerted by the fluid, its flexural rigidity and the tension necessary to enforce the filament inextensibility. For both rigid and deformable bodies, the instantaneous no-slip and impermeability conditions on the solid boundary are imposed via external and localised body forces which are consistently introduced into the Lattice Boltzmann equation. The validation test-cases for rigid bodies include the case of an impulsively started plate and the sedimentation of particles under gravity in a fluid initially at rest. For the case of deformable slender structures we consider the beating of both a single filament and a pair filaments induced by the interaction with an incoming uniformly streaming flow.
Gokaltun, Seckin; McDaniel, Dwayne; Roelant, David
2012-07-01
Multiphase flows involving gas and liquid phases can be observed in engineering operations at various Department of Energy sites, such as mixing of slurries using pulsed-air mixers and hydrogen gas generation in liquid waste tanks etc. The dynamics of the gas phase in the liquid domain play an important role in the mixing effectiveness of the pulsed-air mixers or in the level of gas pressure build-up in waste tanks. To understand such effects, computational fluid dynamics methods (CFD) can be utilized by developing a three-dimensional computerized multiphase flow model that can predict accurately the behavior of gas motion inside liquid-filled tanks by solving the governing mathematical equations that represent the physics of the phenomena. In this paper, such a CFD method, lattice Boltzmann method (LBM), is presented that can model multiphase flows accurately and efficiently. LBM is favored over traditional Navier-Stokes based computational models since interfacial forces are handled more effectively in LBM. The LBM is easier to program, more efficient to solve on parallel computers, and has the ability to capture the interface between different fluid phases intrinsically. The LBM used in this paper can solve for the incompressible and viscous flow field in three dimensions, while at the same time, solve the Cahn-Hillard equation to track the position of the gas-liquid interface specifically when the density and viscosity ratios between the two fluids are high. This feature is of primary importance since the previous LBM models proposed for multiphase flows become unstable when the density ratio is larger than 10. The ability to provide stable and accurate simulations at large density ratios becomes important when the simulation case involves fluids such as air and water with a density ratio around 1000 that are common to many engineering problems. In order to demonstrate the capability of the 3D LBM method at high density ratios, a static bubble simulation is
NASA Astrophysics Data System (ADS)
Salehi, H.; Aryadoust, M.; Shoushtari, M. Zargar
2014-07-01
In this paper, the propagation of acoustic waves in the phononic crystal of 3D with rhombohedral(I) lattice is studied theoretically. The crystal composite constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of Brillouin zone. In the present work, we have investigated the effect of lattice angle on the band structure and width of the band gap rhombohedral(I) lattice in the irreducible part of the first Brillouin zone and its planes separately. The results show that more than one complete band gape are formed in the four planes of the irreducible part. The most complete band gaps are formed in the (111) plane and the widest complete band gap in (443) with an angle greater than 80. So, if the sound passes through the (111) and (443) planes for the lattice angle close to 90, the crystal phononic displays the excellent insulation behavior. Moreover, in the other planes, the lattice angle does not affect on the width and the number of band gaps. Also, for the filling fraction 5 %, the widest complete band gap is formed. These results are consistent with the effect of symmetry on the band gap width, because the (111) plane has the most symmetry.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered
NASA Astrophysics Data System (ADS)
Halliday, I.; Lishchuk, S. V.; Spencer, T. J.; Pontrelli, G.; Evans, P. C.
2016-08-01
We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013), 10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.
Single qubit gates on neutral atoms in a 3d Optical lattice
NASA Astrophysics Data System (ADS)
Kumar, Aishwarya; Wang, Yang; Zhang, Xianli; Corcovilos, Theodore A.; Weiss, David S.
2015-05-01
Neutral atoms are especially promising candidates for quantum computing because of their inherent scalability. To realize this scalability requires being able to manipulate the quantum information at target qubits with high fidelity and low crosstalk. We will present two single qubit gate addressing protocols. We have experimentally applied them both to targeted sites in a 5 × 5 × 5 3D array. The two distinct approaches both use crossed MEMS-mirror directed addressing beams along with microwave pulses to target atoms at single sites, while having minimal impact on the quantum information at non-target sites. Supported by DARPA, QUEST and ARO.
Electromagnetic Scattering of Finite and Infinite 3D Lattices in Polarizable Backgrounds
Gallinet, Benjamin; Martin, Olivier J. F.
2009-10-07
A novel method is elaborated for the electromagnetic scattering from periodical arrays of scatterers embedded in a polarizable background. A dyadic periodic Green's function is introduced to calculate the scattered electric field in a lattice of dielectric or metallic objects. The method exhibits strong advantages: discretization and computation of the field are restricted to the volume of the scatterers in the unit cell, open and periodic boundary conditions for the electric field are included in the Green's tensor, and finally both near and far-fields physics are directly revealed, without any additional computational effort. Promising applications include the design of periodic structures such as frequency-selective surfaces, photonic crystals and metamaterials.
NASA Astrophysics Data System (ADS)
Ghanbarian, Behzad; Daigle, Hugh; Hunt, Allen G.; Ewing, Robert P.; Sahimi, Muhammad
2015-01-01
Understanding and accurate prediction of gas or liquid phase (solute) diffusion are essential to accurate prediction of contaminant transport in partially saturated porous media. In this study, we propose analytical equations, using concepts from percolation theory and the Effective Medium Approximation (EMA) to model the saturation dependence of both gas and solute diffusion in porous media. The predictions of our theoretical approach agree well with the results of nine lattice Boltzmann simulations. We find that the universal quadratic scaling predicted by percolation theory, combined with the universal linear scaling predicted by the EMA, describes diffusion in porous media with both relatively broad and extremely narrow pore size distributions.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-03-01
In this paper, a numerical method for the modeling of shallow waters interacting with slender elastic structures is presented. The fluid domain is modeled through the lattice Boltzmann method, while the solid domain is idealized by corotational beam finite elements undergoing large displacements. Structure dynamics is predicted by using the time discontinuous Galerkin method and the fluid-structure interface conditions are handled by the Immersed Boundary method. An explicit coupling strategy to combine the adopted numerical methods is proposed and its effectiveness is tested by computing the error in terms of the energy that is artificially introduced at the fluid-solid interface.
Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability
NASA Astrophysics Data System (ADS)
Ginzburg, Irina; Roux, Laetitia
2015-10-01
The Taylor dispersion in parabolic velocity field provides a well-known benchmark for advection-diffusion (ADE) schemes and serves as a first step towards accurate modeling of the high-order non-Gaussian effects in heterogeneous flow. While applying the Lattice Boltzmann ADE two-relaxation-times (TRT) scheme for a transport with given Péclet number (Pe) one should select six free-tunable parameters, namely, (i) molecular-diffusion-scale, equilibrium parameter; (ii) three families of equilibrium weights, assigned to the terms of mass, velocity and numerical-diffusion-correction, and (iii) two relaxation rates. We analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a Gaussian plume. For this purpose, the third- and fourth-order transient multi-dimensional analysis of the recurrence equations of the TRT ADE scheme is extended for a spatially-variable velocity field. The key point is in the coupling of the truncation and Taylor dispersion analysis which allows us to identify the second-order numerical correction δkT to Taylor dispersivity coefficient kT. The procedure is exemplified for a straight Poiseuille flow where δkT is given in a closed analytical form in equilibrium and relaxation parameter spaces. The predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range. In relatively small Pe-range, the relative dispersion error increases with Péclet number. This deficiency reduces in the intermediate and high Pe-range where it becomes Pe-independent and velocity-amplitude independent. Eliminating δkT by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries, the d2Q9 TRT ADE scheme may reproduce the Taylor-Aris result quasi-exactly, from very coarse to fine grids, and from very small to arbitrarily high Péclet numbers. Since free-tunable product of two
Pore-Scale Study of Miscible Displacements in Porous Media Using Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Zhang, Ting; Shi, Baochang; Huang, Changsheng; Liang, Hong
2015-12-01
In the past few years, the miscible displacements in porous media were usually simulated by some semiempirical models based on the volume averaging at the representative elementary volume scale. To better understand the microscopic mechanism of the viscous fingering phenomenon in porous media for miscible fluids, in this paper the miscible displacements processes in porous media are studied using the lattice Boltzmann method (LBM) at the pore scale. First, the code of LBM is tested by simulating the displacement process of two miscible fluids with the same viscosity between two parallel plates which is the well-known Taylor-Aris dispersion problem, and comparing the results with the theoretical predictions. Then, the effects of the Péclet number Pe, the viscosity ratio M and the structure of the porous media on the displacement phenomenon are investigated, and the location and velocity of the finger tip, the displacement efficiency are also studied. In this paper, the displacement efficiency is calculated by 1-m, here the quantity m is defined as m=V_M/V_T, where V_M is the volume of more viscous fluids (the displaced fluid) left behind the finger tip, V_T is the total pore volume behind the finger tip. It can be found that the "interface" of two fluids will become clearer with the increasing of the Péclet number. As Pe and M are large enough, the viscous fingering phenomenon will occur, and in the front of the finger, "mushroom-like" pattern can be observed. Besides, with the increasing of Pe or M the quantity m will be increased too, i.e., the displacement efficiency will be decreased. While Pe (or M) is greater than a certain value, the growth rate of the quantity m will slow down. The same trend was observed for the miscible displacement in capillary tubes or Hele-Shaw cells. Besides, changing the structure of the porous media makes the finger pattern different. The present simulation results provide a good understanding of the microscopic mechanism of the
Li, Qiuxiang; Chai, Zhenhua; Shi, Baochang; Liang, Hong
2014-10-01
In this paper, we present a numerical study on the deformation and breakup behavior of liquid droplet past a solid circular cylinder by using an improved interparticle-potential lattice Boltzmann method. The effects of the eccentric ratio β, viscosity ratio λ between the droplet and the surrounding fluid, surface wettability, and Bond number (Bo) on the dynamic behavior of the liquid droplet are considered. The parameter β represents the degree that the solid cylinder deviates from the center line, and Bo is the ratio between the inertial force and capillary force. Numerical results show that there are two typical patterns, i.e., breakup and no breakup, which are greatly influenced by the aforementioned parameters. When β increases to a critical value βc, the droplet can pass the circular cylinder without a breakup, otherwise, the breakup phenomenon occurs. The critical eccentric ratio βc increases significantly with increasing Bo for case with λ>1, while for the case with λ<1, the viscosity effects on the βc is not obvious when Bo is large. For the breakup case, the amount of deposited liquid on the tip of the circular cylinder is almost unaffected by β. In addition, the results also show that the viscosity ratio and wettability affect the deformation and breakup process of the droplet. For case with λ<1, the viscosity ratio plays a minor role in the thickness variations of the deposited liquid, which decreases to a nonzero constant eventually; while for λ>1, the increase of the viscosity ratio significantly accelerates the decrease of the deposited liquid, and finally no fluid deposits on the cylinder. In term of the wettability, there occurs continuous gas phase trapped by the wetting droplet, but this does not happen for nonwetting droplet. Besides, for λ<1, the time required to pass the cylinder (tp) decreases monotonically with decreasing contact angle, while a nonmonotonic decrease appears for λ>1. It is also found that tp decreases
Li, Bai; Lin, Mu; Liu, Qiao; Li, Ya; Zhou, Changjun
2015-10-01
Protein folding is a fundamental topic in molecular biology. Conventional experimental techniques for protein structure identification or protein folding recognition require strict laboratory requirements and heavy operating burdens, which have largely limited their applications. Alternatively, computer-aided techniques have been developed to optimize protein structures or to predict the protein folding process. In this paper, we utilize a 3D off-lattice model to describe the original protein folding scheme as a simplified energy-optimal numerical problem, where all types of amino acid residues are binarized into hydrophobic and hydrophilic ones. We apply a balance-evolution artificial bee colony (BE-ABC) algorithm as the minimization solver, which is featured by the adaptive adjustment of search intensity to cater for the varying needs during the entire optimization process. In this work, we establish a benchmark case set with 13 real protein sequences from the Protein Data Bank database and evaluate the convergence performance of BE-ABC algorithm through strict comparisons with several state-of-the-art ABC variants in short-term numerical experiments. Besides that, our obtained best-so-far protein structures are compared to the ones in comprehensive previous literature. This study also provides preliminary insights into how artificial intelligence techniques can be applied to reveal the dynamics of protein folding. Graphical Abstract Protein folding optimization using 3D off-lattice model and advanced optimization techniques. PMID:26381910
2013-01-01
Background Proteins are essential biological molecules which play vital roles in nearly all biological processes. It is the tertiary structure of a protein that determines its functions. Therefore the prediction of a protein's tertiary structure based on its primary amino acid sequence has long been the most important and challenging subject in biochemistry, molecular biology and biophysics. In the past, the HP lattice model was one of the ab initio methods that many researchers used to forecast the protein structure. Although these kinds of simplified methods could not achieve high resolution, they provided a macrocosm-optimized protein structure. The model has been employed to investigate general principles of protein folding, and plays an important role in the prediction of protein structures. Methods In this paper, we present an improved evolutionary algorithm for the protein folding problem. We study the problem on the 3D FCC lattice HP model which has been widely used in previous research. Our focus is to develop evolutionary algorithms (EA) which are robust, easy to implement and can handle various energy functions. We propose to combine three different local search methods, including lattice rotation for crossover, K-site move for mutation, and generalized pull move; these form our key components to improve previous EA-based approaches. Results We have carried out experiments over several data sets which were used in previous research. The results of the experiments show that our approach is able to find optimal conformations which were not found by previous EA-based approaches. Conclusions We have investigated the geometric properties of the 3D FCC lattice and developed several local search techniques to improve traditional EA-based approaches to the protein folding problem. It is known that EA-based approaches are robust and can handle arbitrary energy functions. Our results further show that by extensive development of local searches, EA can also be very
Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji
2014-07-01
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme. PMID:25122406