• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Nuclear Engineering and Technology
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• v.52 no.7
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• pp.1347-1354
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• 2020

To improve the efficiency of MC criticality calculation, an acceleration method of fission source convergence which gives an improved initial fission source is proposed. In this method, the MC global homogenization is carried out to obtain the macroscopic cross section of each material mesh, and then the nonlinear iterative solution of the SP3 equations is used to determine the fission source distribution. The calculated fission source is very close to the real fission source, which describes its space and energy distribution. This method is an automatic computation process and is tested by the C5G7 benchmark, the results show that this acceleration method is helpful to reduce the inactive cycles and overall running time.