Neutron transport solution using the Daubechies' wavelets in the spatial discretization

This paper describes a one-dimensional wavelet-based spatial discretization scheme for the first-order neutron transport equation. Two special features are introduced: i) the spatial variable is discretized using the Daubechies' wavelets on the interval, and the neutron flux is represented in term of the wavelet series in a normalized node, the tradition SN angular discretization scheme is used in solving the equation, and ii) the wavelet Galerkin method is applied here, using the Daubechies' scaling function as both the trialing function and weighting function, the integrations of Daubechies' scaling function and its derivative in the Galerkin system are calculated numerically, using the difference quotient instead of the derivative. The boundary conditions and interface conditions are given in the exact form of wavelets series and added into the Galerkin system in special locations. The LU decomposition method is applied to solving the matrix in formed in the Galerkin system. The test results on several benchmark problems indicate that the wavelet-based spatial discretization scheme in this paper is capable of handling the first-order neutron transport equation, accurate in treating the boundary condition while using the wavelets expansion in spatial discretization, effective in treating the transport problems in the deep penetrating medium and in strong heterogeneous medium.