Least-squares spectral element method for radiative heat transfer in semitransparent media

Least-squares spectral element method based on the discrete-ordinate equation is developed to solve multidimensional radiative heat transfer problems in semitransparent media. An efficient algorithm for implementation of the method is presented. Chebyshev polynomials are employed as basis functions for the spectral element discretization. The p-convergence characteristics of the least-squares spectral element method are studied. The convergence rate is very fast and approximately follows the exponential law. Four test problems are taken as examples to verify the least-squares spectral element formulation. The predicted temperature distributions and radiative heat flux are determined by the least-squares spectral element method and compared with data in the references. The results show that the least-squares spectral element method developed in this article has good accuracy for solving multidimensional radiative heat transfer problems.