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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.
A highperformance lattice Boltzmann implementation to model flow in porous media
, 2004
"... We examine the problem of simulating single and multiphase flow in porous medium systems at the pore scale using the lattice Boltzmann (LB) method. The LB method is a powerful approach, but one which is also computationally demanding; the resolution needed to resolve fundamental phenomena at the ..."
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Cited by 12 (1 self)
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We examine the problem of simulating single and multiphase flow in porous medium systems at the pore scale using the lattice Boltzmann (LB) method. The LB method is a powerful approach, but one which is also computationally demanding; the resolution needed to resolve fundamental phenomena at the pore scale leads to very large lattice sizes, and hence substantial computational and memory requirements that necessitate the use of massively parallel computing approaches. Common LB implementations for simulating flow in porous media store the full lattice, making parallelization straightforward but wasteful. We investigate a twostage implementation consisting of a sparse domain decomposition stage and a simulation stage that avoids the need to store and operate on lattice points located within a solid phase. A set of five domain decomposition approaches are investigated for single and multiphase flow through both homogeneous and heterogeneous porous medium systems on di#erent parallel computing platforms. An orthogonal recursive bisection method yields the best performance of the methods investigated, showing near linear scaling and substantially less storage and computational time than the traditional approach.
Threedimensional effect of the effective thermal conductivity of porous media
 Journal of Physics D: Applied Physics
"... A threedimensional mesoscopic method is developed for predicting the effective thermal conductivity of multiphase random porous media. The energy transport equations are solved by a lattice Boltzmann method for multiphase conjugate heat transfer through a porous structure whose morphology is charac ..."
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Cited by 8 (2 self)
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A threedimensional mesoscopic method is developed for predicting the effective thermal conductivity of multiphase random porous media. The energy transport equations are solved by a lattice Boltzmann method for multiphase conjugate heat transfer through a porous structure whose morphology is characterized by a random generationgrowth algorithm. Our numerical results show that the cell number in the third dimension influences the resulting effective thermal conductivity of threedimensional porous media. The predicted effective thermal conductivity varies with the cell number in the third dimension following an exponential relationship, and it requires in the examples at least 10 cells along the third dimension before the predictions stabilize. Comparisons with the experimental data show that the effective thermal conductivities measured by the hotprobe and hotwire techniques agree well with the predicted results by the twodimensional model, whereas those measured by the transient comparative method agree more with the threedimensional predictions. 1.
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.
Quantitative analysis of numerical estimates for the permeability of porous media from latticeBoltzmann simulations
 Journal of Statistical Mechanics
, 2010
"... Abstract. During the last decade, latticeBoltzmann simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, wellknown improvements of the original algorithm are often not implemented. These include, for example, multirelaxation ..."
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Cited by 5 (1 self)
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Abstract. During the last decade, latticeBoltzmann simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, wellknown improvements of the original algorithm are often not implemented. These include, for example, multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature.
A lattice Boltzmann Method for Immiscible Multiphase Flow Simulations using the Level Set Method
, 2009
"... This work has been supported by DFG grants JU 440/13, STE 871/1 and ..."
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Cited by 4 (0 self)
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This work has been supported by DFG grants JU 440/13, STE 871/1 and
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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Lattice BGK simulations of flow in a symmetric bifurcation
, 2004
"... Surgical planning as a treatment for vascular diseases requires fast blood flow simulations that are efficient in handling changing geometry. It is, for example, necessary to try different paths of a planned bypass and study the resulting hemodynamic flow fields before deciding the final geometrical ..."
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Cited by 4 (0 self)
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Surgical planning as a treatment for vascular diseases requires fast blood flow simulations that are efficient in handling changing geometry. It is, for example, necessary to try different paths of a planned bypass and study the resulting hemodynamic flow fields before deciding the final geometrical solution. With the aid of a real time interactive simulation environment that uses an efficient flow solver, this allows flexible treatment planning. In this article, we demonstrate that the lattice Boltzmann method can be an alternative robust computational fluid dynamics technique for such kind of applications. Steady flow in a 2D symmetric bifurcation is studied and the obtained flow fields and stress tensor components are compared to those obtained by a NavierStokes (NS) solver. We also demonstrate that the method is fully adaptive to interactively changing geometry.