On the Analytical Solution of the S_NRadiative Transport Equation in a Slab for a Space-dependent Albedo Coefficient

Abstract

Abstract. In this work, we report a genuine general analytical solution for the linearized SN radiative-conductive transfer problem in a heterogeneous plane parallel atmosphere with the albedo coefficient depending continuously on the spatial variable. By general solution, we mean that the solution is valid for an arbitrary albedo coefficient continuous functions of the spatial variable having the property of fulfill the requirements of existence and uniqueness. The key feature of this novel approach embodies the steps: following the idea of the Decomposition method, we transform the original problem into a set of recursive problems with constant albedo coefficients, having the main feature that the sources terms takes the information of the spatial dependency of the albedo coefficient into account. This procedure allows us to solve, analytically, the resulting recursive system by the LTSN method developed for a constant albedo coefficient. Finally, we present the error control analysis of the solution and numerical comparisons against the literature results.

Integral Methods in Science and Engineering

“…Further, we resort to the decomposition method recently applied successfully to a similar type of problem [PeEtAl11a]. Other works along this line may be found in [BoEtAl10], [Ce10], [PeEtAl11b], [Pe11], [AzEtAl11], [BoEtAl12], [SeViGo12], [VaSeVi12].…”