Lattice Boltzmann Boundary Conditions for Flow, Convection-Diffusion and MHD Simulations (2506.00907v1)

Abstract: A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment-conservations are proposed to enforce the boundary conditions with given macroscopic quantities, including the velocity and pressure boundary conditions in flow simulations, a given concentration in convection-diffusion (CD) simulations, as well as specified magnetic field components in magnetohydrodynamical (MHD) simulations. Additionally, the CD and MHD simulations might involve the Robin boundary condition for surface reactions and a Robin-like boundary condition for thin walls with finite electrical conductivities, respectively, both of which can be written in a form with a variable flux term. In this case, the proposed boundary scheme takes the flux term as an increment to the bounced distribution function and a reference frame transformation is used to obtain a correction term for moving boundaries. Spatial interpolation and extrapolation are used for arbitrary boundary locations between computational grid points. Due to using the same approach in derivations, the derived boundary conditions for different physical processes in a coupled simulation are compatible for arbitrary boundary-to-grid distances (not limited to the popular half-grid boundary layout) and arbitrary moving speeds (not limited to the tangential or normal speed). Simulations using half-grid and full-grid boundary layouts are conducted for demonstrations and validations. Moving boundaries are simulated in hydrodynamic and MHD flows, while static boundaries are used in the CD simulations with surface reactions. The numerical and analytical solutions are in excellent agreement in the studied cases.