A general single-node second-order boundary condition for the lattice Boltzmann method

Abstract

In this work, we propose a general single-node nonslip hydrodynamic boundary condition for the lattice Boltzmann method. The construction of the boundary scheme is the combination of the bounce back rule for the nonequilibrium part of the density distribution and linear interpolation. The proposed boundary condition is very simple, universal, stable, and accurate. The asymptotic analysis of the newly proposed boundary condition confirms that is of second-order accuracy. The numerical experiments demonstrate that the boundary condition is indeed second-order accurate for both straight and curved boundaries.

Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows

“…To give one example, the Central Linear (CLI) scheme [57] prescribes α (u) (δ) from the physical consistency parametrization condition, without restoring the corresponding interpolation. We will show that the interpolations with an adjustable length l, such as ZLI and CHLI recently introduced by Zhao et al [61] and Chen et al [62], can be transformed into specific dependencies α (u) (δ, l ); they reduce to YLI-type schemes [22,56,63] when l = δ, and to the Second-Order Single-Node (SSN) rule [64] when l = 2δ.…”

“…The first technique was proposed [59] for all links with the up- stream fluid neighbor; we call these algorithms single-node methods. The second technique was adopted [59] when an upstream neighbor is missing; more recent three-population interpolations [22,[61][62][63][64][65] adopt this approach for all cut links and allow one to update unknown populations already in a modified collision step. This last property is shared by the local-single-node methods, which employ only local outgoing populations and nonequilibrium corrections.…”

A Novel Lattice Boltzmann Scheme with Single Extended Force Term for Electromagnetic Wave Propagating in One-Dimensional Plasma Medium

“…It has been widely used for various types of linear and non-linear PDEs, such as diffusion [24], flow [25], waves [26], quantum mechanics [27][28][29] and heat transfer [30,31]. Moreover, with advanced LBM technique, such as the immersed boundary-LBM method, LBM has also been used to determine hydrodynamic force and energy exchange problems among particle and flow [32,33]. Given the paramount role of EM phenomena in science and technology, it is of great interest to investigate whether the LBM is able to improve simulations of complex EM phenomena.…”

A New Lattice Boltzmann Scheme for Photonic Bandgap and Defect Mode Simulation in One-Dimensional Plasma Photonic Crystals

“…As a general numerical simulation method, the lattice Boltzmann method (LBM) has achieved considerable success in various applications in the last two decades, since it divides all simulators into two decoupling parts: streaming and colliding parts [32]. The former, streaming parts, can easily be implemented with a memory swap function, while the latter, colliding parts, are totally reliant on the data of the local cell without using the data from the adjacent cells; which enables them to exhibit excellent scalability and easy implementation [33], as well as to be widely used in solving a vast range of partial differential equations, including fluid flow [34], wave [35], quantum mechanics [36][37][38], and heat transfer [39][40][41][42][43] problems. Due to the LBM's excellent performance in previous areas, there is considerable interest in investigating the applicability and capability of such a method in solving EM waves in 1D plasma PhCs.…”