Discontinuous spectral element method for radiative heat transfer in axisymmetric cylindrical medium

Abstract

The discontinuous spectral element method (DSEM) is extended to solve the discrete ordinates form of radiative transfer equation (RTE) in axisymmetric cylindrical enclosures. The DSEM combines the traits of the discontinuous finite element method (DFEM) and the spectral methods. It permits the discontinuity of variables across the element boundaries and can offer hp-convergence. The Chebyshev polynomials are employed to construct the nodal basis functions, and the piecewise constant angular (PCA) quadrature is used for the angular discretization. The performance of the DSEM is investigated. Results show that for 1-D problems, its p-convergence rate is very fast, following the exponential law, but its h-convergence rate is only second-order. For 2-D problems, the p and h convergence rates drop to second and first order respectively. Considering the CPU time, the DSEM shows advantage over the discrete ordinates method (DOM) only for 1-D problems, while, for 2-D problems, its performance is something worse than that of DOM. A problem with discontinuous boundary conditions is investigated. The results of DSEM suffer from severe ray effect when the number of discrete directions is inadequate. By applying angular refinement, the ray effect can be mitigated availably and satisfactory solutions can be obtained. Besides, the DSEM is applied to solving a problem with moderate complex geometry, and results show that the present method can obtain accurate solutions.