Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

We introduce two new approaches, called A-LSOB and N-MR, for boundary interface-conjugate conditions on flat or curved surface shapes in the advection-diffusion lattice Boltzmann method (LBM). The Local Second-Order, single-node enhances existing Dirichlet Neumann normal treatments with respect to locality, accuracy, Péclet parametrization. normal-multi-reflection (N-MR) improves directional flux schemes via a local release of their nonphysical tangential constraints. N-MR restore all first- second-order derivatives from nodal non-equilibrium solution, they are conditioned be exact piece-wise parabolic profile uniform arbitrary-oriented velocity field. Additionally, most compact accurate diffusion flow grid-inclined pipes introduced. In simulations, global mass-conservation solvability condition steady-state, two-relaxation-time (S-TRT) formulation is adjusted either (i) mass-source (ii) corrective surface-flux. conclude that surface-flux counterbalance more than bulk one, ones high regime, (iii) advective-diffusive scheme shows best conservation properties then performance both no-slip interface-perpendicular flow, (iv) diffusive extrapolation least conserving accurate. error dependency, invariance over an additive constant, truncation isotropy guide this analysis. Our methodology extends d2q9 isotropic S-TRT 3D anisotropic matrix collisions, Robin condition, transient LBM.