Migration of a van der Waals bubble: Lattice Boltzmann formulation

Holdych, David J.; Georgiadis, John G.; Buckius, Richard O.

doi:10.1063/1.1352625

Cited by 30 publications

(5 citation statements)

References 19 publications

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“…These fluid flow models have been used to simulate formidable problems such as flows of suspensions [26] and porous media flows [28,35]. Additionally, LB models have been developed to simulate multiphase and multicomponent flows [12,20,33,36]. Boltzmann equation.…”

Section: Introductionmentioning

confidence: 99%

Truncation error analysis of lattice Boltzmann methods

Holdych

Noble

Georgiadis

et al. 2004

Journal of Computational Physics

125

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Section: Introductionmentioning

confidence: 99%

Truncation error analysis of lattice Boltzmann methods

Holdych

Noble

Georgiadis

et al. 2004

Journal of Computational Physics

125

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“…), or imaging gradients (slice selection, phase encoding, or readout). Starting with its first application for modeling unrestricted diffusion [63], LBM has since accommodated anisotropic diffusion and advection [64,65], coupled diffusion [50] and coupled reaction-diffusion between multiple species [48,62], finite cell membrane permeability [66], phase field models [67], and interstitial flow [68][69][70]. Such processes are pertinent to biophysics problems involving transport and evolution of large biomolecules in blood-perfused cellular systems, and physics other than diffusion.…”

Section: Discussionmentioning

confidence: 99%

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

2020

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We report the first implementation of the Lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments on skeletal muscle, and to offset the small time step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation in a tissue model consisting of cylindrical inclusions (representing bundles of parallel myocytes), delineated by thin permeable membranes (sarcolemma) and surrounded by a extracellular domain (endomysium). As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. The geometry is discretized in uniform 2D or 3D lattices by locating the curved cylindrical boundaries halfway between lattice nodes. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate that the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system with MPI is straightforward. For a domain decomposition algorithm on one million lattice nodes, the speedup is linear up to 168 MPI processes. While offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a sui generis scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models, and to accommodate sophisticated dMRI sequences.

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“…The free energy model of Swift et al [73] does not suffer from such limitations as in SC model. It has been successfully used to simulate some multiphase flows, such as stationary bubble/droplet, capillary wave, and phase separation in a narrow capillary [73], two-dimensional bubble in Poiseuille flow [77]. However the Galilean invariance cannot be maintained in this model [78].…”

Section: Methodsmentioning

confidence: 99%

Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions

et al. 2010

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Cavitation is often triggered when the fluid pressure is lower than the vapor pressure at a local thermodynamic state. The present article reviews recent progress made toward developing modeling and computational strategies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cavity. The review considers alternative cavitation models along Reynolds-averaged Navier-Stokes and very lager eddy simulation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative importance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cavitation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment.

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Migration of a van der Waals bubble: Lattice Boltzmann formulation

Cited by 30 publications

References 19 publications

Truncation error analysis of lattice Boltzmann methods

Truncation error analysis of lattice Boltzmann methods

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions

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