Thermal boundary condition for the thermal lattice Boltzmann equation

Abstract

A thermal boundary condition for a double-population thermal lattice Boltzmann equation (TLBE) is introduced and numerically demonstrated. The unknown distribution population at the boundary node is decomposed into its equilibrium part and nonequilibrium parts, and then the nonequilibrium part is approximated with a first-order extrapolation of the nonequilibrium part of the populations at the neighboring fluid nodes. Numerical tests with Dirichlet and Neumann boundary constraints show that the numerical results of the TLBE together with the present boundary schemes agree well with the analytical solutions and those of the finite-volume method.