Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method Article Swipe
Liangqi Zhang
,
Shiliang Yang
,
Zhong Zeng
,
Jia Wei Chew
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1103/physreve.97.023302
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1103/physreve.97.023302
In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second-order accuracy. Then, the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming [see the paragraph after Eq. (29) for the discussions of the "streaming step" in LB method]. After that, the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes. For straight boundaries, boundary nodes are directly placed at the physical boundary surface, and the present scheme is applied directly. When extending the present scheme to curved geometries, a local curvilinear coordinate system and first-order Taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface. In essence, the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface. Therefore, the advantages of the present boundary implementations are (i) the locality, i.e., no information from neighboring fluid nodes is required; (ii) the consistency, i.e., the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes, thus the three kinds of conditions are realized in a consistent way. It should be noted that the present focus is on two-dimensional cases, and theoretical derivations as well as the numerical validations are performed in the framework of the two-dimensional five-velocity lattice model.
Related Topics
Concepts
Neumann boundary condition
Lattice Boltzmann methods
Boundary (topology)
Boundary value problem
Robin boundary condition
Mathematical analysis
Mathematics
Mixed boundary condition
Boundary conditions in CFD
Singular boundary method
Dirichlet boundary condition
Physics
Mechanics
Boundary element method
Finite element method
Thermodynamics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physreve.97.023302
- http://link.aps.org/pdf/10.1103/PhysRevE.97.023302
- OA Status
- bronze
- Cited By
- 24
- References
- 77
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2790006959
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2790006959Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1103/physreve.97.023302Digital Object Identifier
- Title
-
Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann methodWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-02-08Full publication date if available
- Authors
-
Liangqi Zhang, Shiliang Yang, Zhong Zeng, Jia Wei ChewList of authors in order
- Landing page
-
https://doi.org/10.1103/physreve.97.023302Publisher landing page
- PDF URL
-
https://link.aps.org/pdf/10.1103/PhysRevE.97.023302Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
bronzeOpen access status per OpenAlex
- OA URL
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https://link.aps.org/pdf/10.1103/PhysRevE.97.023302Direct OA link when available
- Concepts
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Neumann boundary condition, Lattice Boltzmann methods, Boundary (topology), Boundary value problem, Robin boundary condition, Mathematical analysis, Mathematics, Mixed boundary condition, Boundary conditions in CFD, Singular boundary method, Dirichlet boundary condition, Physics, Mechanics, Boundary element method, Finite element method, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
24Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 1, 2023: 4, 2022: 2, 2021: 4Per-year citation counts (last 5 years)
- References (count)
-
77Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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