51. Chebyshev spectral-SN method for the neutron transport equation
- Author
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Asadzadeh, M. and Kadem, A.
- Subjects
- *
DISCRETE ordinates method in transport theory , *SPECTRAL theory , *CHEBYSHEV approximation , *POLYNOMIALS , *GAUSSIAN quadrature formulas - Abstract
Abstract: We study convergence of a combined spectral and (SN) discrete ordinates approximation for a multidimensional, steady state, linear transport problem with isotropic scattering. The procedure is based on expansion of the angular flux in a truncated series of Chebyshev polynomials in spatial variables that results in the transformation of the multidimensional problems into a set of one-dimensional problems. The convergence of this approach is studied in the context of the discrete-ordinates equations based on a special quadrature rule for the scattering integral. The discrete-ordinates and quadrature errors are expanded in truncated series of Chebyshev polynomials of degree ≤ L, and the convergence is derived assuming L ≤ σ t - 4πσ s , where σ t and σ s are total- and scattering cross-sections, respectively. [Copyright &y& Elsevier]
- Published
- 2006
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