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43
Lattice Boltzmann method for 3D flows with curved boundary
 J. Comput. Phys
"... In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary condition ..."
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Cited by 53 (1 self)
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In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamic 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 3D implementations. Three athermal 3D LBE models (Q15D3, Q19D3, and Q27D3) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hänel (1998, J. Comp.
An accurate curved boundary treatment in the lattice Boltzmann method
 J. Comput. Phys
, 1999
"... The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving hydrodynamics for various systems. Major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Because ..."
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Cited by 38 (6 self)
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The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving hydrodynamics for various systems. Major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Because the method often uses uniform regular Cartesian lattices in space, curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy. In this work, a secondorder accurate treatment of the boundary condition in the LBE method is developed for a curved boundary. The proposed treatment of the curved boundaries is an improvement of a scheme due to O. Filippova and D. Hänel (1998, J. Comput. Phys. 147, 219). The proposed treatment for curved boundaries is tested against several flow problems: 2D channel flows with constant and oscillating pressure gradients for which analytic solutions are known, flow due to an impulsively started wall, liddriven square cavity flow, and uniform flow over a column of circular cylinders. The secondorder accuracy is observed with a solid boundary arbitrarily placed between lattice nodes. The proposed boundary condition has wellbehaved stability characteristics when the relaxation time is close to 1/2, the zero limit of viscosity. The improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice Boltzmann method. c ○ 1999 Academic Press I.
Corrigendum to ”Lattice PoissonBoltzmann simulations of electroosmotic flows in microchannels
 J. Colloid Interface Sci. 296 (2006) 729736], J. Colloid Interface Sci
"... Abstract. This paper presents numerical analysis of electroosmotic flows (EOF) in charged anisotropic porousmedia using the lattice PoissonBoltzmannmethod (LPBM), which combines two sets of lattice evolution methods solving the nonlinear Poisson equation for electric potential distribution and the ..."
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Cited by 18 (6 self)
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Abstract. This paper presents numerical analysis of electroosmotic flows (EOF) in charged anisotropic porousmedia using the lattice PoissonBoltzmannmethod (LPBM), which combines two sets of lattice evolution methods solving the nonlinear Poisson equation for electric potential distribution and the NavierStokes equations for fluid flow respectively. Consistent boundary condition implementations are proposed for solving both the electrodynamics and the hydrodynamics on a same grid set. The anisotropic structure effects on EOF characteristics are therefore studied by modeling the electrically driven flows through ellipse arrays packed in a microchannel whose shape and orientation angle are used to control the anisotropy of porous media. The results show that flow rates increase with the axis length along the external electric field direction for a certain porosity and decrease with the angle between the semimajor axis and the bulk flow direction when the orientation angle is smaller than π/2. After introducing random factors into the microstructures of porous media, the statistical results of flow rate show that the anisotropy of microstructure decreases the permeability of EOFs in porous media.
Parallel Lattice Boltzmann Methods for CFD Applications
"... The lattice Boltzmann method (LBM) has evolved to a promising alternative to the wellestablished methods based on finite elements/volumes for computational fluid dynamics simulations. Ease of implementation, extensibility, and computational efficiency are the major reasons for LBM’s growing field ..."
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Cited by 11 (9 self)
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The lattice Boltzmann method (LBM) has evolved to a promising alternative to the wellestablished methods based on finite elements/volumes for computational fluid dynamics simulations. Ease of implementation, extensibility, and computational efficiency are the major reasons for LBM’s growing field of application and increasing popularity. In this paper we give a brief introduction to the involved theory and equations for LBM, present various techniques to increase the singleCPU performance, outline the parallelization of a standard LBM implementation, and show performance results. In order to demonstrate the straightforward extensibility of LBM, we then focus on an application in material science involving fluid flows with free surfaces. We discuss the required extensions to handle this complex scenario, and the impact on the parallelization technique.
Progress in lattice Boltzmann methods for magnetohydrodynamic flows relevant to fusion applications
, 2007
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Lattice Boltzmann Method for Modeling LiquidVapor Interface
 Configurations in Porous Media,” Water Resources Research
"... [1] The lattice Boltzmann method (LBM) has emerged as a powerful tool for simulating the behavior of multiphase fluid systems in complex pore networks. Specifically, the single component multiphase LBM can simulate the interfacial phenomena of surface tension and adsorption and thus be used for mode ..."
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Cited by 6 (1 self)
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[1] The lattice Boltzmann method (LBM) has emerged as a powerful tool for simulating the behavior of multiphase fluid systems in complex pore networks. Specifically, the single component multiphase LBM can simulate the interfacial phenomena of surface tension and adsorption and thus be used for modeling fluids such as water and its vapor in porous media. This paper provides an introduction to LBM applications to interface configurations in partially saturated porous media. Key elements of this LBM application are fluidfluid and fluidsolid interactions that successfully mimic the YoungLaplace equation and liquid film adsorption. LBM simulations of liquid behavior in simple pore geometry considering capillarity and adsorption are in good agreement with analytical solutions and serve as critical first steps toward validating this approach. We demonstrate the usefulness of LBM in constructing virtual liquid retention measurements based on porous media imagery. Results of this study provide a basis for application of LBM to understanding liquid configurations in more complex geometries and clear a path for applications involving interface migration, flow, and transport in partially saturated porous
Lattice Boltzmann Simulations of 2D Laminar Flows past Two Tandem Cylinders
, 2008
"... We apply the lattice Boltzmann equation (LBE) with multiplerelaxationtime (MRT) collision model to simulate laminar flows in twodimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched nonuniform mesh and inflow and outfl ..."
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Cited by 5 (0 self)
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We apply the lattice Boltzmann equation (LBE) with multiplerelaxationtime (MRT) collision model to simulate laminar flows in twodimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched nonuniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of nonuniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRTLBE. The MRTLBE with nonuniform 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 a unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRTLBE method with grid stretching.
A Thermal Lattice Boltzmann TwoPhase Flow Model and Its Application to Heat Transfer Problems—Part 1. Theoretical Foundation,”
 ASME J. Fluids Eng.,
, 2006
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A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip, Int
 J. Numer. Meth. Fluids
"... This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multicomponent model use ..."
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Cited by 3 (0 self)
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This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multicomponent model used in the subsequent chapters. Commonly used single component LB methods use a nonphysical equation of state, in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multicomponent systems containing gases of differing molecular masses that are modelled with the ideal gas equation of state. Also, existing methods for implementing boundary conditions are unsuitable for extending to novel boundary conditions, such as diffusion slip. Therefore, a new single component LB derivation and a new method for implementing boundary conditions are developed, and validated against Poiseuille flow. However, including a physical equation of state reduces stability and time accuracy, leading to longer computational times, compared with ‘incompressible ’ LB methods. The new method of analysing LB boundary conditions successfully explains observations from other commonly used schemes, such as the slip velocity associated with ‘bounceback’. The new model developed for multicomponent gases avoids the pitfalls of some other LB models, a single computational grid is shared by all the species and the diffusivity is independent of the viscosity. The NavierStokes equation for the mixture and the StefanMaxwell diffusion equation are both recovered by the model. However, the species momentum equations are not recovered correctly and this can lead to instability. Diffusion slip, the nonzero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple onedimensional model for channel flow. To increase the accuracy of the scheme a second order numerical implementation is needed. This can be achieved using a variable transformation method which does not result in an increase in computational time.
A lattice Boltzmann method for shock wave propagation in solids
"... This paper proposes a new lattice Boltzmann (LB) method for the study of shock wave propagation in elastic solids. The method, which implements a fluxcorrected transport (FCT) algorithm, contains three stages: collision, streaming, and correction. In the collision stage, distribution functions are ..."
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This paper proposes a new lattice Boltzmann (LB) method for the study of shock wave propagation in elastic solids. The method, which implements a fluxcorrected transport (FCT) algorithm, contains three stages: collision, streaming, and correction. In the collision stage, distribution functions are updated. In the streaming stage, the distribution functions are shifted between lattice points. Generally, a partial differential equation (PDE) is solved in the streaming stage, and finite element methods are employed to support the use of unstructured meshes in the LB method. The FCT algorithm is used in the correction stage to revise the distribution functions at lattice points, so fluctuations behind shock wave fronts can be eliminated efficiently. In this method, schemes for shock wave reflection at fixed and free boundaries are developed based on the bounceback technique. A similar technique is used to treat wave reflection and transmission at material interfaces of composites. Several onedimensional examples show that this LBFCT method can provide ideal depictions of shock wave propagation in structures, especially composite structures.