A Coupled Discrete Unified Gas-Kinetic Scheme for Convection Heat Transfer in Porous Media

Abstract

In this paper, the discrete unified gas-kinetic scheme (DUGKS) is extended to the convection heat transfer in porous media at representative elementary volume (REV) scale, where the changes of velocity and temperature fields are described by two kinetic equations. The effects from the porous medium are incorporated into the method by including the porosity into the equilibrium distribution function, and adding a resistance force in the kinetic equation for the velocity field. The proposed method is systematically validated by several canonical cases, including the mixed convection in porous channel, the natural convection in porous cavity, and the natural convection in a cavity partially filled with porous media. The numerical results are in good agreement with the benchmark solutions and the available experimental data. It is also shown that the coupled DUGKS yields a second-order accuracy in both temporal and spatial spaces.