The Lattice Boltzmann method and computational analysis of bone dynamics-I

Javed, Sana; Sohail, Ayesha; Maqbool, Khadija; Butt, Saad Ihsan; Chaudhry, Qasim Ali

doi:10.1186/s40294-017-0051-1

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…After substituting Equations (15)- (17) into Equation 14, equating the coefficients of δt with various orders results for the order (δt) 0 in:…”

Section: Recovery Of the Navier-stokes Equationsmentioning

confidence: 99%

“…Since then, the study of the lattice Boltzmann method and the applications of the method have received extensive attentions, making it become a very powerful modelling tool in many areas such as thermodynamics [12], aerodynamics [13], multiphase flows [14], turbulent flows [15], hemodynamics [16], biomechanics [17], image analysis [18], biology [19] and environmental science [20].…”

Section: Introductionmentioning

confidence: 99%

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Macroscopic Lattice Boltzmann Method

Zhou

2020

Water

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The lattice Boltzmann method (LBM) is a highly simplified model for fluid flows using a few limited fictitious particles. It has been developed into a very efficient and flexible alternative numerical method in computational physics, demonstrating its great power and potential for resolving more and more challenging physical problems in science and engineering covering a wide range of disciplines such as physics, chemistry, biology, material science and image analysis. The LBM is implemented through the two routine steps of streaming and collision using the three parameters of the lattice size, particle speed and collision operator. A fundamental question is if the two steps are integral to the method or if the three parameters can be reduced to one for a minimal lattice Boltzmann method. In this paper, it is shown that the collision step can be removed and the standard LBM can be reformulated into a simple macroscopic lattice Boltzmann method (MacLAB). This model relies on macroscopic physical variables only and is completely defined by one basic parameter of the lattice size δx, bringing the LBM into a precise “lattice” Boltzmann method. The viscous effect on flows is naturally embedded through the particle speed, making it an ideal automatic simulator for fluid flows. Three additional advantages compared to the existing LBMs are that: (i) physical variables can directly be retained as the boundary conditions; (ii) much less computational memory is required; and (iii) the model is unconditionally stable. The findings are demonstrated and confirmed with numerical tests including flows that are independent of and dependent on fluid viscosity, 2D and 3D cavity flows and an unsteady Taylor–Green vortex flow. This provides an efficient and powerful model for resolving physical problems in various disciplines of science and engineering.

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“…After substituting Equations (15)- (17) into Equation 14, equating the coefficients of δt with various orders results for the order (δt) 0 in:…”

Section: Recovery Of the Navier-stokes Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Macroscopic Lattice Boltzmann Method

Zhou

2020

Water

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show abstract

“…hemodynamics [16], biomechanics [17], image analysis [18], biology [19], environmental science [20].…”

mentioning

confidence: 99%

Macroscopic Lattice Boltzmann Method (MacLAB)

Zhou

2019

Preprint

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The birth of the lattice Boltzmann method (LBM) fulfils a dream that simple arithmetic calculations can simulate complex fluid flows without solving complicated partial differential flow equations. Its power and potential of resolving more and more challenging physical problems have been and are being demonstrated in science and engineering covering a wide range of disciplines such as physics, chemistry, biology, material science and image analysis.

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