On anti bounce back boundary condition for lattice Boltzmann schemes

Autor: François Dubois, Mohamed Mahdi Tekitek, Pierre Lallemand
Přispěvatelé: Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), Conservatoire National des Arts et Métiers [CNAM] (CNAM), Beijing Computational Science Research Center [Beijing] (CSRC), Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis (FST), Université de Tunis El Manar (UTM)
Rok vydání: 2020
Předmět:
Asymptotic analysis
linear acoustic
Lattice Boltzmann methods
FOS: Physical sciences
Boundary (topology)
Physics - Classical Physics
010103 numerical & computational mathematics
01 natural sciences
Physics::Fluid Dynamics
FOS: Mathematics
[NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
Mathematics - Numerical Analysis
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
Boundary value problem
0101 mathematics
Boundary cell
Mathematics
heat equation
Mathematical analysis
Classical Physics (physics.class-ph)
Numerical Analysis (math.NA)
Hagen–Poiseuille equation
Taylor expansion method PACS numbers: 0270Ns
0520Dd
010101 applied mathematics
Computational Mathematics
Computational Theory and Mathematics
Flow (mathematics)
Modeling and Simulation
4710+g
Heat equation
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Computers & Mathematics with Applications
Computers & Mathematics with Applications, Elsevier, 2020, ⟨10.1016/j.camwa.2019.03.039⟩
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2019.03.039
Popis: International audience; In this contribution, we recall the derivation of the anti bounce back boundary condition for the D2Q9 lattice Boltzmann scheme. We recall various elements of the state of the art for anti bounce back applied to linear heat and acoustics equations and in particular the possibility to take into account curved boundaries. We present an asymptotic analysis that allows an expansion of all the fields in the boundary cells. This analysis based on the Taylor expansion method confirms the well known behaviour of anti bounce back boundary for the heat equation. The analysis puts also in evidence a hidden differential boundary condition in the case of linear acoustics. Indeed, we observe discrepancies in the first layers near the boundary. To reduce these discrepancies, we propose a new boundary condition mixing bounce back for the oblique links and anti bounce back for the normal link. This boundary condition is able to enforce both pressure and tangential velocity on the boundary. Numerical tests for the Poiseuille flow illustrate our theoretical analysis and show improvements in the quality of the flow.
Databáze: OpenAIRE
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