Chebyshev spectral-S-N method for the neutron transport equation
We study convergence of a combined spectral and (S-N) 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 <=sigma(t)-4 pi sigma(s), where sigma(t) and sigma(s) are total and scattering cross-sections, respectively. (c) 2006 Elsevier Ltd. All rights reserved.
isotropic scattering convergence analysis linear transport equation chebyshev spectral method discrete-ordinates method