A one‐point second‐order Dirichlet boundary condition for the thermal lattice Boltzmann method

Abstract

AbstractA one‐point second‐order Dirichlet boundary condition for convection‐diffusion equation based on the lattice Boltzmann method has been proposed. The unknown temperature distribution is interpolated from the distributions at the wall node and fluid node nearest to the wall in the direction of the lattice velocity. At the wall node, the unknown temperature distribution is expressed as a summation of equilibrium and nonequilibrium distributions. The equilibrium distribution is obtained using the wall temperature, while the nonequilibrium distribution is approximated from the nearest fluid node in the direction of the lattice velocity. Both asymptotic analysis and numerical simulations of heat conduction indicate that the Dirichlet boundary condition is second‐order accurate. Further comparisons demonstrate that the newly proposed boundary method is sufficiently accurate to simulate natural convection, convective and unsteady heat transfer involving straight and curved boundaries.