An improvement of the double discrete ordinate approximation solution by Laplace technique for radiative-transfer problems without azimuthal symmetry and high degree of anisotropy

Abstract

One-dimensional radiative-transfer problems without azimuthal symmetry and with a high degree of anisotropy are solved using the double discrete ordinate approximation methods LTA N and ALTA N . The discussed methods start with projecting out azimuthal components of the original equation and results in an equation system. Then the collocation method is applied to the polar angle and the integral is approximated by a Gaussian quadrature scheme that yields the S N transport equation system. The subsequent application of the Laplace transform in the spatial variable opens pathways for application of the specific procedures that characterise the LTA N and the ALTA N methods. The results are solutions for the radiative-transport problem. We further report on numerical simulations and comparisons with the LTS N method.

Non-Linear Radiative-Conductive Heat Transfer in a Heterogeneous Gray Plane-Parallel Participating Medium

“…The latter case turns Adomian obsolete, because the non-linear term vanishes, whereas ω = 0 diagonalizes the equation system and thus turns Laplace obsolete, since the solution may be obtained directly by integration. The decomposition method as originally introduced is designed for general non-linear problems, but several ways are possible to construct a solution (Cardona et al, 2009;Segatto et al, 2008). The present study may be considered a guideline on how to distribute the influence of the boundary conditions and the non-linearity in order to solve the given problem.…”

Improved naive Bayes classification algorithm for traffic risk management

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Improved Naive Bayes Classification Algorithm for Traffic Risk Management

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