A finite element approach for treating the energy variable in the numerical solution of the neutron transport equation

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Abstract
A finite element method is applied to the first order form of the energy-dependent neutron transport equation. The energy variable is treated separately from the position and direction variables. This treatment leads to a set of multigroup equations that generalize the standard multigroup equations. An error analysis is performed in which the error with respect to the energy variable is separated from the error with respect to the position and direction variables. The analysis indicates that the error in the standard multigroup equations is proportional to the width of the energy intervals, i.e. groups. The accuracy can be increased by using the generalized multigroup equations that are derived in the present investigation. (A disadvantage is that they are more complicated than the standard multigroup equations.) Numerical examples indicate that the accuracy obtained using these generalized multigroup equations is about the same as that obtained using the standard multigroup-equations but with eight times the number of energy intervals at least for moderately deep shield in gpenetrations.