Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number

Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru

doi:10.1063/1.869426

Cited by 101 publications

(61 citation statements)

References 15 publications

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“…As mentioned in section 3, there is a restriction in the Prandtl number in the LBM-coupled model as given by Eq. (19). Hence, a high value was assigned to ν in this study.…”

Section: Macrosegregation Simulationmentioning

confidence: 99%

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Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Ohno

Sato

2018

ISIJ Int.

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Lattice Boltzmann Method (LBM), newly developing technique of computational fluid dynamics, is coupled with solute and energy conservation equations to develop a macrosegregation simulation model (LBM-coupled model) with high computational efficiency. LBM does not require time-consuming calculations for correction of velocity and pressure of fluid in contrast to methods directly solving Navier-Stokes (NS) equation and, therefore, LBM is computationally efficient. In this study, the accuracy of the LBMcoupled model is investigated by calculating the steady state flows and by comparing the results with those of analytical solutions and a conventional model based on the NS equation. The results between them are almost identical with each other and it indicates that the accuracy of the LBM-coupled model is sufficiently high. Moreover, a macrosegregation simulation is carried out for a simple case where the macrosegregation emerges only by natural convection, by means of the LBM-coupled and conventional models. The LBM-coupled model yields almost the same result with the one of NS-based model. Importantly, however, the simulation of LBM-coupled model is about five times faster than the one of NS-based model.

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“…As mentioned in section 3, there is a restriction in the Prandtl number in the LBM-coupled model as given by Eq. (19). Hence, a high value was assigned to ν in this study.…”

Section: Macrosegregation Simulationmentioning

confidence: 99%

“…[14][15][16][17][18][19][20] It is a newly developing technique of computational fluid dynamics. LBM describes the time evolution of particle distribution function, from which one can calculate the macroscopic quantities such as the density, velocity and pressure of fluid.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Ohno

Sato

2018

ISIJ Int.

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“…This is the same scaling that leads from the Boltzmann equation directly to the incompressible Navier-Stokes equations in the small Mach number limit at fixed Reynolds number. It was adopted by Inamuro et al [49] in a lattice Boltzmann context, following earlier work in continuum kinetic theory collected in the book by Sone [50].…”

Section: Quantum Cellular Automatamentioning

confidence: 99%

Quantum lattice algorithms: similarities and connections to some classic finite difference algorithms

Dellar¹

2015

ESAIM: Proc.

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Abstract. Quantum lattice algorithms originated with the Feynman checkerboard model for the onedimensional Dirac equation. They offer discrete models of quantum mechanics in which the complex numbers representing wavefunction values on a discrete spatial lattice evolve through discrete unitary operations. This paper draws together some of the identical, or at least unitarily equivalent, algorithms that have appeared in three largely disconnected strands of research. Treated as conventional numerical algorithms, they are all only first order accurate under refinement of the discrete space/time grid, but may be raised to second order by a unitary change of variables. Much more efficient implementations arise from replacing the evolution through a sequence of unitary intermediate steps with a short path integral formulation that expresses the wavefunction at each spatial point on the most recent time level as a linear combination of values at immediately preceding time levels and neighbouring spatial points. In one dimension, a particularly elegant reformulation replaces two variables at two time levels with a single variable over three time levels. The resulting algorithm is a variational integrator arising from a discrete action principle, and coincides with the Ablowitz-Kruskal-Ladik finite difference scheme for the Klein-Gordon equation.

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“…The dimensionless kinematic viscosity ν of the fluid and the dimensionless mass diffusivity D BA in the binary miscible fluid mixture are given by [22] …”

Section: Asymptotic Analysismentioning

confidence: 99%