Improved rational approximation for spatially-dependent resonance self-shielding in CASMO5

Recently, a new Spatially-Dependent resonance Self-Shielding (SDSS) method was developed and implemented into CASMO5 within the framework of Equivalence Theory. An Optimal Two-Term Rational (OTTR) approximation for the Stoker-Weiss treatment of concentric annular fuel regions yielded an adequate approximation for fuel-to-fuel collision probabilities for a subdivided cylindrical fuel region. Reference fuel-to-fuel probabilities, obtained by performing a series of fixed-source, two-dimensional transport calculations, are used in searching for optimal coefficients to the rational approximation. Three search algorithms are evaluated in this work with the goal of obtaining the best practical accuracy at minimal computational cost. An improved formulation of SDSS is proposed and tested to further reduce the error of the rational approximation, especially for the outer rings of the fuel pellet. Numerical results are presented which provide a comparison of various choices for search algorithms and confirm the improved accuracy obtained by using the new proposed formulation for the rational approximation. The Levenberg-Marquardt and Nelder-Mead methods both perform well, with a small advantage to Nelder-Mead for its slightly shorter runtimes. The 6-degrees-of-freedom (dof) rational approximation achieves significantly better accuracy (up to an 8 times error reduction at the pellet rim) than the previous 3-dof model. (authors)