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 characteristic line length of the modified SDUGKS establishes a relationship with the Courant-Friedrichs-Lewy (CFL) number in the DUGKS, which guarantees the accuracy of the modified SDUGKS. Furthermore, the characteristic line length is no longer limited by the extinction coefficient like in original SDUGKS. As a result, the modified SDUGKS is more accurate and robust than original SDUGKS, and more efficient than the 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.

翻译：在这项工作中,建议采用稳定离散的统一气体动能办法(SDUGKS),以解决稳定的辐射转移方程式(RTE),这是对原SDUGKS[X.F.Zhou等人,J.Comput.Phys. 423,109767(202020年)]的改进。除了原SDUGKS使用的矩形规则外,在重建细胞界面之间的能量通量的拟议方法中采用了固定离散的统一气体动能办法(SDUGKS)。因此,修改后的SDUGKS的特性线长比原SDUGKS更准确、更坚固。 修改后的SDUGKS的特性线长与原Surant-Friedriedrichs-Lewy(CL)的原始SDUGKS(X)数字阵列(X.X.X.F.F.F.F.F.F.F.F.F.F.F.C.C.C.C.P.L.S.S.)的数字关系,这保证了修改后的SDUDUGKKS.L.S.S.S.S.