Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport

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@article{e6ae0e6ea3404871863d1e2fec1af5e7,
title = "Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport",
abstract = "The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high P´eclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-`a-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.",
keywords = "Single relaxation time, lattice Boltzmann formulation, convection-diffusion, diffusion velocity, anisotropic behaviour, porous media",
author = "Janez Perko and Ravi Patel",
note = "Score = 10",
year = "2014",
month = "5",
doi = "10.1103/PhysRevE.89.053309",
language = "English",
volume = "E89",
pages = "1--9",
journal = "Physical Review B",
issn = "1098-0121",
publisher = "APS - American Physical Society",
number = "5",

}

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TY - JOUR

T1 - Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport

AU - Perko, Janez

AU - Patel, Ravi

N1 - Score = 10

PY - 2014/5

Y1 - 2014/5

N2 - The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high P´eclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-`a-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.

AB - The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high P´eclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-`a-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.

KW - Single relaxation time

KW - lattice Boltzmann formulation

KW - convection-diffusion

KW - diffusion velocity

KW - anisotropic behaviour

KW - porous media

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_136517

UR - http://knowledgecentre.sckcen.be/so2/bibref/11751

U2 - 10.1103/PhysRevE.89.053309

DO - 10.1103/PhysRevE.89.053309

M3 - Article

VL - E89

SP - 1

EP - 9

JO - Physical Review B

JF - Physical Review B

SN - 1098-0121

IS - 5

ER -

ID: 335756