Analysis of the lattice kinetic Monte Carlo method in systems with external fields

Lee, Young Ki; Sinno, Talid

doi:10.1063/1.4972052

Cited by 3 publications

(4 citation statements)

References 37 publications

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“…In fact, this presents the main motivation for the second-order, central-difference-based TDRW scheme proposed here. Very recently and for the same reasons, Lee and Sinno [22] suggested an improved treatment of advective fluxes in the LKMC method. Specifically, they chose to employ an approximation, known as the exponential scheme in the finite-volume context, which suffers less from the numerical diffusion but is not guaranteed to provide second-order accuracy in general.…”

Section: Numerical Propertiesmentioning

confidence: 99%

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Modeling mass transfer in fracture flows with the time domain-random walk method

2019

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The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous matrix. Simulations with several flow rates, diffusion coefficients, and matrix porosities indicate good agreement between the numerical approximations and analytical solutions.

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Section: Numerical Propertiesmentioning

confidence: 99%

“…[13,38]. Lee and Sinno [22] very recently revisited this scheme and proposed an improvement constructed starting from a microscopic premise. Here, the flux terms are computed using an approximation known as the exponential scheme in the finite-volume context.…”

Section: Introductionmentioning

confidence: 99%

Modeling mass transfer in fracture flows with the time domain-random walk method

2019

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“…This information could be used to develop patient-specific evaluations of cardiovascular risk or response to therapy. Looking ahead, even larger length and timescale simulations will require additional computational strategies, such as further optimization of parallelization algorithms, the use of novel massively parallel hardware architectures (e.g., GPUs), or the use of non-uniform adaptive grids for the LKMC and LB modules [16,47].…”

Section: Frontiers In Physicsmentioning

confidence: 99%

Development of a parallel multiscale 3D model for thrombus growth under flow

Shankar,

Diamond,

Sinno

2023

Front. Phys.

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Thrombus growth is a complex and multiscale process involving interactions spanning length scales from individual micron-sized platelets to macroscopic clots at the millimeter scale. Here, we describe a 3D multiscale framework to simulate thrombus growth under flow comprising four individually parallelized and coupled modules: a data-driven Neural Network (NN) that accounts for platelet calcium signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. Parallelization was achieved by developing in-house parallel routines for NN and LKMC, while the open-source libraries OpenFOAM and Palabos were used for FVM and LB, respectively. Importantly, the parallel LKMC solver utilizes particle-based parallel decomposition allowing efficient use of cores over highly heterogeneous regions of the domain. The parallelized model was validated against a reference serial version for accuracy, demonstrating comparable results for both microfluidic and stenotic arterial clotting conditions. Moreover, the parallelized framework was shown to scale essentially linearly on up to 64 cores. Overall, the parallelized multiscale framework described here is demonstrated to be a promising approach for studying single-platelet resolved thrombosis at length scales that are sufficiently large to directly simulate coronary blood vessels.

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“…The kinetic constants depend on the diffusivity of the species considered. 48 To ensure that the selected transition rates capture correctly the dynamical evolution of the system towards equilibrium, one can consider the Boltzmann relationship…”

Section: Theoretical Backgroundmentioning

confidence: 99%

A kinetic Monte Carlo approach to study fluid transport in pore networks

Apostolopoulou

Day

Hull

et al. 2017

The Journal of Chemical Physics

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The mechanism of fluid migration in porous networks continues to attract great interest. Darcy's law (phenomenological continuum theory), which is often used to describe macroscopically fluid flow through a porous material, is thought to fail in nano-channels. Transport through heterogeneous and anisotropic systems, characterized by a broad distribution of pores, occurs via a contribution of different transport mechanisms, all of which need to be accounted for. The situation is likely more complicated when immiscible fluid mixtures are present. To generalize the study of fluid transport through a porous network, we developed a stochastic kinetic Monte Carlo (KMC) model. In our lattice model, the pore network is represented as a set of connected finite volumes (voxels), and transport is simulated as a random walk of molecules, which "hop" from voxel to voxel. We simulated fluid transport along an effectively 1D pore and we compared the results to those expected by solving analytically the diffusion equation. The KMC model was then implemented to quantify the transport of methane through hydrated micropores, in which case atomistic molecular dynamic simulation results were reproduced. The model was then used to study flow through pore networks, where it was able to quantify the effect of the pore length and the effect of the network's connectivity. The results are consistent with experiments but also provide additional physical insights. Extension of the model will be useful to better understand fluid transport in shale rocks.

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Analysis of the lattice kinetic Monte Carlo method in systems with external fields

Cited by 3 publications

References 37 publications

Modeling mass transfer in fracture flows with the time domain-random walk method

Modeling mass transfer in fracture flows with the time domain-random walk method

Development of a parallel multiscale 3D model for thrombus growth under flow

A kinetic Monte Carlo approach to study fluid transport in pore networks

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