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

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