An improved three-dimensional wavelet-based method for solving the first-order Boltzmann transport equation

A new angular discretization scheme based on the Daubechies' wavelets has been developed in recent studies. A decoupled S_N and wavelet expansion method was proposed. This paper discusses the limitations and improvements of this decoupled scheme. The scaling function, instead of the wavelet function, is applied as the basis function. It significantly improved the efficiency and computational stability. A new series of wavelets on the interval are applied instead of the 'wrapped wavelets', which eliminate the edge effect in the angular subdomain scheme. Based on the improvements, a wavelet-based neutron transport code package WAVTRAN is developed and the previous work is extended to the three-dimensional calculation and anisotropic scattering calculation. Numerical results demonstrate that the improvements are effective. Further investigations demonstrate that the wavelet-based angular discretization scheme is more powerful than the traditional ones in some highly anisotropic angular flux problems.