Non-linear boundary conditions for the convection-diffusion equation in lattice Boltzmann framework. (16th January 2022)

• Record Type: Journal Article
• Authors: Kashani, Elham; Mohebbi, Ali; Feili Monfared, Amir Ehsan; Raoof, Amir
• Is Part Of: Chemical engineering science. Volume 247(2022)
• Publication Date: 2022-01-16
• Subjects: Lattice Boltzmann method -- Convection-diffusion -- Non-linear Robin boundary condition -- Radiation -- Nth-order surface reaction -- Fracture; Chemical engineering -- Periodicals; Génie chimique -- Périodiques; Chemical engineering; Periodicals; Electronic journals; 660
• DOI: 10.1016/j.ces.2021.116925
• Languages: English
• ISSNs: 0009-2509

Abstract

Graphical abstract: Highlights: A method for the implementation of Robin boundary condition in 2D LBM is introduced. The method suggests using a coupling of Taylor expansion and counter-slip approach. The method can impose nonlinear reaction kinetics in lattice Boltzmann framework. The method can impose surface radiation condition in lattice Boltzmann framework. Order of convergence rate is a function of the nonlinearity of the condition. Abstract: Implementation of nonlinear boundary conditions like n th -order surface reactions or surface radiation heat transfer has not been investigated in lattice Boltzmann (LB) framework. This study presents a novel kinetic level method for their implementation. The method couples Taylor expansion of the conditions with counter-slip approach to find unknown distribution functions at boundary nodes. The proposed scheme guarantees the locality and orientation independency of formulations. To evaluate the proposed scheme performance, several 1D and 2D test cases were simulated by D2Q9 LBM and the outcomes were compared with analytical and numerical solutions. The geometry evolution by n th -order surface reaction was investigated for dissolutions in a simple fracture and a spherical carbonate particle in a channel. The results demonstrated the method performs promisingly in terms of accuracy. The convergence rate of scheme based on the results from l 2 -norm analyses showed first or second-order rates of convergence, depending on constraint's degree of nonlinearity.