Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport
Abstract
The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) and multiple-relaxation-time (MRT) collision operators has been widely used in simulating flow and transport phenomena. However, it is well known that the SRT LBM is prone to numerical instability for small relaxation rate while the selection of relaxation parameters in the MRT LBM is challenging. By contrast, the LBM based on two-relaxation-time (TRT) collision operators embodies advantages of the SRT LBM for simple implementation and of the MRT LBM for good numerical stability. However, the TRT LBM has not been widely used. One reason is that the tedious mathematical derivations and presentations of the TRT LBM impede its understanding and implementation. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in the subsurface environments, including advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability for these transport phenomena in both simple and complicated geometries. Therefore, the TRT LBM provides powerful potential to simulatemore »
- Authors:
-
[1];
- Tianjin Univ., Tianjin (China). Inst. of Surface-Earth System Science
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Columbia Univ., New York, NY (United States). Dept. of Environmental Health Sciences
- Publication Date:
- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER)
- OSTI Identifier:
- 1395283
- Alternate Identifier(s):
- OSTI ID: 1844595
- Report Number(s):
- PNNL-SA-125138
Journal ID: ISSN 0309-1708; PII: S0309170816307680
- Grant/Contract Number:
- AC05-76RL01830; P30 ES009089; 2016YFA0601000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Advances in Water Resources
- Additional Journal Information:
- Journal Volume: 109; Journal ID: ISSN 0309-1708
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; 54 ENVIRONMENTAL SCIENCES; Lattice Boltzmann Method; Two-Relaxation-Time; Pore-scale model; Advection-diffusion; Reactive transport; Porous media; lattice-Boltzmann method, reactive transport in porous media, subsurface environments
Citation Formats
Yan, Zhifeng, Yang, Xiaofan, Li, Siliang, Scheibe, Timothy, and Hilpert, Markus. Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport. United States: N. p., 2017.
Web. doi:10.1016/J.ADVWATRES.2017.09.003.
Yan, Zhifeng, Yang, Xiaofan, Li, Siliang, Scheibe, Timothy, & Hilpert, Markus. Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport. United States. https://doi.org/10.1016/J.ADVWATRES.2017.09.003
Yan, Zhifeng, Yang, Xiaofan, Li, Siliang, Scheibe, Timothy, and Hilpert, Markus. Tue .
"Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport". United States. https://doi.org/10.1016/J.ADVWATRES.2017.09.003. https://www.osti.gov/servlets/purl/1395283.
@article{osti_1395283,
title = {Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport},
author = {Yan, Zhifeng and Yang, Xiaofan and Li, Siliang and Scheibe, Timothy and Hilpert, Markus},
abstractNote = {The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) and multiple-relaxation-time (MRT) collision operators has been widely used in simulating flow and transport phenomena. However, it is well known that the SRT LBM is prone to numerical instability for small relaxation rate while the selection of relaxation parameters in the MRT LBM is challenging. By contrast, the LBM based on two-relaxation-time (TRT) collision operators embodies advantages of the SRT LBM for simple implementation and of the MRT LBM for good numerical stability. However, the TRT LBM has not been widely used. One reason is that the tedious mathematical derivations and presentations of the TRT LBM impede its understanding and implementation. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in the subsurface environments, including advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability for these transport phenomena in both simple and complicated geometries. Therefore, the TRT LBM provides powerful potential to simulate various geophysical and biochemical behaviors in the subsurface environments.},
doi = {10.1016/J.ADVWATRES.2017.09.003},
journal = {Advances in Water Resources},
number = ,
volume = 109,
place = {United States},
year = {Tue Sep 05 00:00:00 EDT 2017},
month = {Tue Sep 05 00:00:00 EDT 2017}
}
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