A diffusion synthetic acceleration method for steady discrete unified gas kinetic scheme in radiative heat transfer

Abstract

An efficient synthetic-type iterative method is proposed to improve the convergence rate of the steady discrete unified gas kinetic scheme (SDUGKS) for steady radiative heat transfer problems. The key ingredient of the present method is the tight coupling of the mesoscopic radiative transfer equation (RTE) and the macroscopic diffusion equation. The RTE is calculated by SDUGKS, and the diffusion equation is solved to predict the incident radiation energy and angular radiation intensity used in SDUGKS to accelerate the evolution, unlike the original diffusion synthetic acceleration (DSA) method which only predicts the incident radiation energy. Furthermore, a damping factor is adopted to remedy the inconsistency of spatial discretization between the mesoscopic SDUGKS and macroscopic diffusion equation. The theoretical convergence rate of the present method is studied via the discrete Fourier analysis. Several numerical tests under a wide range of optical thicknesses are performed to show the convergence speed. The damping factor and the correction of the angular radiation intensity added in solving the macroscopic diffusion equation greatly increase the stability of the present method and also reduce its computational costs. The convergence rate of the present method becomes faster than that of previous SDUGKS when the optical thickness is larger than 10. With the increase of extinction coefficient, the speedup ratio of the present method and SDUGKS in one-dimensional problems becomes extremely large and also reaches one or two orders of magnitude in two- and three-dimensional problems.