A.V. Cardona

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTSN) methods applied to the radiative transfer equation in the discrete ordinates (SN) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” SN problems by using the LTSN method. We show some numerical experiments for a typical model problem.

Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

Abstract In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations.

A solution of the linear transport equation using Walsh function and Laplace transform

Abstract In this work the Walsh functions and the Laplace transform are combined to solve, analytically, the one-group linear transport equation in a planar geometry considering anisotropic scattering. Numerical simulations are presented.

General solution of one-dimensional approximations to the transport equation

Abstract The aim of this work is to present a complete review of the generic method for solving analytically one-dimensional approximations of the transport equation that appear as a set of first order linear differential equations, employing the Laplace transfrom technique over a finite domain. Recent advances are also included.

Solutions to the multidimensional linear transport equation by the spectral method

The spectral method is used to develop a solution for multidimensional transport problems for neutral particles in cartesian geometry. The procedure is based on the expansion of the angular flux in a truncated series of orthogonal polynomials that results in the transformation of the multidimensional problem into a set of one-dimensional problems, whose solutions are well established. The convergence of this approach is studied in the context of the multidimensional discrete-ordinates equations.

A recursive method to invert the LTSN matrix

In this work it is presented a recursive method to invert the LTSN matrix. Numerical simulations are presented.

On the decomposition method applied to linear and non-linear discrete ordinates problems in slab geometry

Abstract We describe the applications of the decomposition method to discrete ordinates (S N ) problems in slab geometry, which model neutral particle transport in shields, and coupled conductive-radiative heat transfer phenomena. Numerical results to typical model problems are shown to illustrate the accuracy of each application.

A comparative study of analytical solutions for some one-dimensional transport equation approximations

Abstract The aim of this work is to study the numerical performance of the W N , Ch N , A N and LD N methods to solve one-dimensional transport problems. Numeral comparisons for small and large thickness slab are presented.

The State-of-the-Art of the LTAN Method in the Solution of the Transport Equation in a Slab

In this work we report the state-of-the-art of the LTAN method, reporting the derivation of the LTAN homogeneous and particular solution in a slab for large N (N < 650), as well its accelerated version, which reduces drastically the computational time. We also sketch the mathematical background for the error bound estimate and convergence analysis of the LTAN method. Finally, we display numerical results and comments.Copyright