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16
A Quantum LatticeGas Model for Computational Fluid Dynamics
, 1999
"... Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a ..."
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Cited by 16 (4 self)
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Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a quantum lattice gas. An analytical treatment of the microscopic quantum latticegas system is carried out to predict its behavior at the mesoscopic and macroscopic scales. At the mesoscopic scale, a lattice Boltzmann equation, with a nonlocal collision term that depends on the entire system wavefunction, governs the dynamical system. Numerical results obtained from an exact simulation of a onedimensional quantum latticemodel are included to illustrate the formalism. A symbolic mathematical method is used to implement the quantum mechanical model on a conventional workstation. The numerical simulation indicates that classical viscous damping is not present in the onedimensional quantum la...
Threedimensional multirelaxation time (MRT) LatticeBoltzmann Models for Multiphase Flow
, 2008
"... In this paper, threedimensional (3D) multirelaxation time (MRT) latticeBoltzmann (LB) models for multiphase flow are presented. In contrast to the BhatnagarGrossKrook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle po ..."
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Cited by 14 (3 self)
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In this paper, threedimensional (3D) multirelaxation time (MRT) latticeBoltzmann (LB) models for multiphase flow are presented. In contrast to the BhatnagarGrossKrook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the ChapmanEnskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the LaplaceYoung relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.
Nonequilibrium entropy limiters in lattice Boltzmann methods
, 2008
"... We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite vo ..."
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Cited by 6 (3 self)
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We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity — nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy “trimming”) and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimation of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D liddriven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100 × 100 grid. All limiter constructions are applicable both for entropic and for nonentropic equilibria.
Entropic Lattice Boltzmann Method for Microflows. http://xxx.lanl.gov/abs/condmat/0412555
, 2004
"... A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice BhatnagarGrossKrook (ELBGK) ..."
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A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice BhatnagarGrossKrook (ELBGK) is studied in detail in order to quantify its relevance for microflow simulations. ELBGK is equipped with boundary conditions which are derived from molecular models (diffusive wall). A map of threedimensional kinetic equations onto twodimensional models is established which enables twodimensional simulations of quasitwodimensional flows. The ELBGK model is studied extensively in the simulation of the twodimensional Poiseuille channel flow. Results are compared to known analytical and numerical studies of this flow in the setting of the BhatnagarGrossKrook model. The ELBGK is in quantitative agreement with analytical results in the domain of weak rarefaction (characterized by Knudsen number Kn, the ratio of mean free path to the hydrodynamic scale), up to Kn ∼ 0.01, which is the domain of many practical microflows. Moreover, the results qualitatively agree throughout the entire Knudsen number range, demonstrating Knudsen’s minimum for the mass flow rate at moderate values of Kn, as well as the logarithmic scaling at large Kn. The present results indicate that ELBM can complement or even replace computationally expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number hydrodynamics pertinent to microflows. 1
MHD turbulence studies using Lattice Boltzmann algorithms
 Comm. Comput. Phys
"... Abstract. Three dimensional freedecaying MHD turbulence is simulated by lattice Boltzmann methods on a spatial grid of 80003 for low and high magnetic Prandtl number. It is verified that ∇·B = 0 is automatically maintained to machine accuracy throughout the simulation. Isosurfaces of vorticity and ..."
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Abstract. Three dimensional freedecaying MHD turbulence is simulated by lattice Boltzmann methods on a spatial grid of 80003 for low and high magnetic Prandtl number. It is verified that ∇·B = 0 is automatically maintained to machine accuracy throughout the simulation. Isosurfaces of vorticity and current show the persistence of many large scale structures (both magnetic and velocity) for long times — unlike the velocity isosurfaces of NavierStokes turbulence.
Nonexistence of H Theorem for Some Lattice Boltzmann Models
, 2004
"... In this paper, we provide a set of sufficient conditions under which a lattice Boltzmann model does not admit an H theorem. By verifying the conditions, we prove that a number of existing lattice Boltzmann models does not admit an H theorem. These models include D2Q6, D2Q9 and D3Q15 athermal models, ..."
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In this paper, we provide a set of sufficient conditions under which a lattice Boltzmann model does not admit an H theorem. By verifying the conditions, we prove that a number of existing lattice Boltzmann models does not admit an H theorem. These models include D2Q6, D2Q9 and D3Q15 athermal models, and D2Q16 and D3Q40 thermal (energyconserving) models. The proof does not require the equilibria to be polynomials. KEY WORDS: Lattice Boltzmann equation; Htheorem. 1.
An introduction to entropic lattice Boltzmann scheme
 SIMAI eLect. Notes
, 2008
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MultipleRelaxationTime Lattice Boltzmann Method for Multiphase Flows with High Density and Viscosity Ratios 10135
"... ABSTRACT In this paper, the lattice Boltzmann method is reviewed for specific applications to numerical simulation of multiphase flow problems. A thorough literature review regarding the multiphase lattice Boltzmann method was conducted with special focus on flows with large density and viscosity ..."
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ABSTRACT In this paper, the lattice Boltzmann method is reviewed for specific applications to numerical simulation of multiphase flow problems. A thorough literature review regarding the multiphase lattice Boltzmann method was conducted with special focus on flows with large density and viscosity ratios between the two phases. A multiphase model with the capability of handling largedensityratios is crucial for the modeling efforts at Florida International University since Department of Energy related operations such as the pulsedair mixing involve air bubbles formed in tanks where the liquid to gas density ratio is approximately 1000. It was observed that there have been four major interface tracking methods developed in the lattice Boltzmann framework, namely; the color method, the freeenergy method, ShanChen's potential method and the indexfunction method. There have also been other methods proposed such as the hybrid levelset lattice Boltzmann method and the fronttracking lattice Boltzmann method, however, they have not been applied as extensively as the others. Lattice Boltzmann simulations are reported to be unstable when the density ratio between fluids are larger than 10. Of twentysix papers reviewed on multiphase lattice Boltzmann method with the singlerelaxationtime collision model, five have extended the capability of the multiphase methods into fluids with largedensityratios up to 1000. However, the singlerelaxationtime lattice Boltzmann method using the BhatnagarGrossKrook collision model was found to have stability issues when the viscosity of the fluid is reduced or the Reynolds number is increased. Lattice Boltzmann method using the multiplerelaxationtime collision operator was proposed by researchers in order to simulate flows where viscosities are low or the Reynolds number is large. Twentyfive publications were reviewed on multiplerelaxationtime methods, seventeen of which were specific to multiphase flows. Six of the multiplerelaxationtime papers were focused on multiphase flows with large liquid to gas density ratios, which was identified as another source of numerical instabilities observed in multiphase simulations with the lattice Boltzmann method. The multiplerelaxationtime lattice Boltzmann method coupled with the modified indexfunction approach was observed to be capable of stable simulations of highdensityratio, low viscosity multiphase flows.
Wetting/dewetting transition of twophase flows in nanocorrugated channels
"... Abstract A lattice version of the Boltzmann kinetic equation for describing multiphase flows in nanoand microcorrugated devices is reviewed. To this purpose, the ShanChen Lattice Boltzmann model [Phys. Rev. E 47, 1815] for nonideal fluids is extended to the case of confined geometries with hyd ..."
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Abstract A lattice version of the Boltzmann kinetic equation for describing multiphase flows in nanoand microcorrugated devices is reviewed. To this purpose, the ShanChen Lattice Boltzmann model [Phys. Rev. E 47, 1815] for nonideal fluids is extended to the case of confined geometries with hydrophobic properties on the wall. This extended ShanChen method is applied for the simulation of the wetting/dewetting transition in the presence of nanoscopic grooves etched on the boundaries. This approach permits to retain the essential supramolecular details of fluidsolid interactions without surrendering in fact boostingthe computational efficiency of continuum methods. The method is first validated against the Molecular Dynamics (MD) results of CottinBizonne et al. [Nature Mater. 2, 237 (2003)] and then applied to more complex geometries, hardly accessible to MD simulations. The resulting analysis confirms that surface roughness and capillary effects can promote a sizeable reduction of the flow drag, with a substantial enhancement of the mass flow rates and sliplengths, which can reach up to the micrometric range for highly hydrophobic surfaces.
Under consideration for publication in J. Fluid Mech. 1 Entropic Lattice Boltzmann Study of Hydrodynamics in a Microcavity
, 2004
"... In flows through microdevices the continuum fluid mechanics description often breaks down and higher order corrections to the Navier–Stokes description arise both at the boundaries and in the bulk. The interaction between the flow geometry, rarefaction and compressibility is not completely understoo ..."
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In flows through microdevices the continuum fluid mechanics description often breaks down and higher order corrections to the Navier–Stokes description arise both at the boundaries and in the bulk. The interaction between the flow geometry, rarefaction and compressibility is not completely understood for such flows. Recent advances in computational kinetic theory, such as the entropic lattice Boltzmann method, provide a simple and realistic framework which enable the systematic study of such interactions. We consider a specific example of entropic lattice Boltzmann model and compare it with Grad’s moment system. We show that for the model under consideration, the dispersion relation is closely related to that of Grad’s tenmoment system. We perform a parametric study of the flow in a microcavity, which is a prototype problem, where the deviations from incompressible hydrodynamics can be studied conveniently. Simulation results obtained with the entropic lattice Boltzmann method are compared with those of the Direct Simulation MonteCarlo method. Based on the parametric study, we discuss aspects of the interaction between rarefaction and compressibility. 1.