Daubechies Wavelet Method for Angular Solution of the Neutron Transport Equation

Abstract

This paper describes Daubechies' wavelet method (DWM) for the discretization of the angular variable in the neutron transport equation. Two special features are introduced: (a) the azimuthal angle is discretized using the Daubechies' scaling function as the basis function, while the polar angle is decoupled and discretized using the discrete ordinates in a standard manner, and (b) the construction of Daubechies' wavelets on an interval is used to get around the edge effect between subdomains in the angular variable. In addition, two acceleration methods, namely, coarse mesh rebalance and coarse mesh finite difference, are implemented in DWM. The test results on several benchmark problems indicate that DWM described in this paper is capable of treating transport problems exhibiting angularly complicated behaviors, effective in mitigating ray effect, and versatile in handling transport phenomena in a variety of structured media.