Chebyshev spectral-SN method for the neutron transport equation

✍ Scribed by M. Asadzadeh; A. Kadem

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 789 KB
• Volume: 52
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2005.11.039

✦ Synopsis

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 < a~ -4~rc%, where at and a8 are totaland scattering cross-sections, respectively. (~)