Enhanced single-node lattice Boltzmann boundary condition for fluid flows

Abstract

We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations. The second is to enhance them by limiting the interpolation extension to the proximity of the boundary. Despite its local nature, the resulting method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well-established Bouzidi's scheme for curved walls [M. Bouzidi, M. Firdaouss, and P. Lallemand, Phys. Fluids 13, 3452 ( 2001)]. Among the infinite number of possibilities, we identify several meaningful variants of the method, discerned by their approximation of the second-order nonequilibrium terms and their interpolation coefficients. For each one, we provide two parametrized versions that produce viscosity independent accuracy at steady state. The method proves to be suitable to simulate moving rigid objects or surfaces moving following either the rigid body dynamics or a prescribed kinematic. Also, it applies uniformly and without modifications in the whole domain for any shape, including corners, narrow gaps, or any other singular geometry.

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

“…The original linear schemes, such as BFL 0 [55] and YLI 0 [56], do not respect this property, but they are parametrized within MGLI family [57]. Among the recent ELI schemes [66], the CELI-UQ counterpart of CLI is parametrized; otherwise, the two parametrization corrections, hereafter referred to as K− 1 and K− 2 in Eq. ( 22) are proposed [66].…”

“…Among the recent ELI schemes [66], the CELI-UQ counterpart of CLI is parametrized; otherwise, the two parametrization corrections, hereafter referred to as K− 1 and K− 2 in Eq. ( 22) are proposed [66]. In the present work, LI + 1 generalizes MGLI uniformly for LI + with the help of K−…”

“…This last property is shared by the local-single-node methods, which employ only local outgoing populations and nonequilibrium corrections. The Enhanced Linear (ELI) infinite family [66] belongs to this last group; it is conceived with two outgoing and two reconstructed virtual wall-located (ghost) populations, where NELI employs the nonequilibrium bounce-back wall approximation of the antisymmetric postcollision local component, say n− q , while symmetric SELI copies n− q and central CELI prescribes their mean value n− q = 0. We will reinterpret ELI as a modified collision ELI + 0 , without any ghost-wall reconstruction, due to a specific symmetric postcollision correction Fq = K + ELI n+ q , where an adjustable combination of NELI and SELI then covers the uniform linear ULT and LLI schemes introduced by Tao et al [67] and Liu et al [68], respectively.…”

“…Due to this first feature, they all are inexact even for a straight and diagonal gridaligned Poiseuille Stokes profile, except for specific values (δ) assigned to free-tunable combination of relaxation rates = (τ + − 1 2 )(τ − − 1 2 ), also known as the "magic parameter," giving a kinematic viscosity ν = 1 3 (τ + − 1 2 ) and an adjustable rate τ − for n− q . Namely, this is the property of the -parametrized schemes, such as BB [51], the Magic Linear (MGLI) subfamily [17,58], which includes the recent MSSN parametrization [65], or else K − 1 − ELI and K − 2 − ELI [66]. We will introduce the parametrized subclass LI + 1 ∈ LI + based on the recent revision [69], which makes the directional closure relation force-independent, and then the dependency (δ) the same in the straight and diagonal channels.…”

“…Appendix B addresses the MRT model and closure relations. Appendix C recasts single-node schemes: (1) YLI [56], GLI [63], ZLI [61], CHLI [62], SSN [64], and MSSN [65] to LI 0 ; (2) scheme [70] to WLI ∈ APLI; and (3) ELI [66], ULT [67], and LLI [68] to ELI + . Appendix D 1 builds the TRT BFL-QI 3 and MLS 3 /FH 3 ; Appendix D 2 provides EMR families.…”