Modified steady discrete unified gas kinetic scheme for multiscale radiative heat transfer

Abstract

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than the rectangular rule used in the original SDUGKS is adopted in the proposed method in the reconstruction of energy flux across cell interface, just as the unsteady DUGKS. By this way, the length of the characteristic line of the modified SDUGKS establishes a relationship with the Courant-Friedrichs-Lewy (CFL) number in the transient DUGKS, which guarantees the accuracy of the modified SDUGKS. Furthermore, the length of the characteristic line is no longer limited by the extinction coefficient like in the original SDUGKS. As a result, the modified SDUGKS is more accurate than the original SDUGKS, and more efficient than the transient DUGKS for steady radiation problems. Furthermore, the smooth linear interpolation and the van Leer limiter are used for problems with smooth and discontinuous optical thicknesses, respectively. Several numerical tests with optical thickness varying from optical thin to thick are conducted to validate the present scheme. Numerical results demonstrate that the modified SDUGKS can serve as an effective tool in the study of multiscale steady radiative heat transfer in participating media.