The spherical harmonics method for the multigroup transport equation in x−y geometry

Light transport in biological tissue based on the simplified spherical harmonics equations

“…This greatly increases the complexity of the multi-D P N approximation; for a given odd order N one obtains many extra unknowns and equations than in 1-D. Also, the equations no longer have the relatively simple diffusion character of Eq. (18). For these reasons, the multidimensional P N equations are not widely used.…”

“…Higher-order approximations to the ERT are required, such as the discrete-ordinates (S N ) [15,16] or spherical harmonics (P N ) [15,17,18] approximations, to overcome the limiting constraints of using the diffusion model. Both methods have already been implemented and applied in tissue optics, with promising results [10,19].…”

Nodal collocation method for the multidimensional PL equations applied to neutron transport source problems

“…We consider now the one-group source problem presented by Fletcher (1981Fletcher ( , 1983 and also studied in Kobayashi et al (1986). The system consists of a square of pure absorber, whose side length is 4 cm and it includes a neutron source of strength S = 1/1.44, in a square of (1.2 cm) 2 , as shown in Fig.…”

Analog Computing for a New Nuclear Reactor Dynamic Model Based on a Time-Dependent Second Order Form of the Neutron Transport Equation

“…The first source problem is a one group fixed source problem that has been widely used by Fletcher, Kobayashi and Inanc and is known as Fletcher's problem [22][23][24]. As shown in Fig.…”