On the application of the analytical discrete ordinates method to the solution of nonclassical transport problems in slab geometry

• Published in: Journal of computational physics Vol. 455; p. 110982
• Main Authors: Moraes, L.R.C., Barichello, L.B., Barros, R.C., Vasques, R.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.04.2022; Elsevier Science Ltd
• Subjects: Algorithms; Analytical discrete ordinates method; Approximation; Computational physics; Mathematical analysis; Nonclassical transport; Polynomials; Representations; Slab geometry; Spectra; Spectral approach; Transport equations; Analytical discrete ordinates method; Spectral approach; Nonclassical transport; Slab geometry
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.110982

•We describe the Analytical Discrete Ordinates method (ADO) for non-classical problems.•We provide an analytical expression for the Lk functions considering diffusion problems.•We show potential limitations in the use of the spectral method.•We present numerical results in slab-geometry, confirming the accuracy of the solution generated using the ADO method.•We show that in certain cases it is required to use extended precision when solving the discretized system of equations. In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generates, as outcome, a system of equations that have the form of classical transport equations and can therefore be solved by current deterministic algorithms. Thus, the investigation of efficient approaches to solve the nonclassical transport equation is of interest and shall be pursued. This is the case of the ADO method which has been successfully used to solve a wide class of problems in the general area of particle transport. Numerical results are presented for two nonclassical test problems in slab geometry. These nonclassical transport problems are chosen in such way that their solution exactly reproduces the solution of the classical diffusion problem. Very accurate results are obtained for both test problems. However, the use of high precision arithmetic is sometimes required as illustrated in the second test problem. Limitations of the spectral approximation are also analyzed and discussed.