Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

2005 ◽  
Vol 1 (4) ◽  
pp. 279
Author(s):  
S.M. Khaled ◽  
Z. Szatmary
Keyword(s):  
Diffusion Equation ◽  
Numerical Method ◽  
Three Dimensional ◽  
Time Dependent ◽  
Neutron Diffusion ◽  
Neutron Diffusion Equation

scholarly journals ADAPTIVE TIME-STEP CONTROL FOR THE MODAL METHOD TO INTEGRATE THE MULTIGROUP NEUTRON DIFFUSION EQUATION

2021 ◽  
Vol 247 ◽  
pp. 07010
Author(s):  
A. Carreño ◽  
A. Vidal-Ferràndiz ◽  
D. Ginestar ◽  
G. Verdú
Keyword(s):  
Diffusion Equation ◽  
Time Dependent ◽  
Local Perturbation ◽  
Neutron Diffusion ◽  
Shape Functions ◽  
Step Size ◽  
Time Step ◽  
Multigroup Neutron ◽  
Neutron Diffusion Equation ◽  
Modal Method

The distribution of the power inside a reactor core can be described by the time dependent multigroup neutron diffusion equation. One of the approaches to integrate this time-dependent equation is the modal method, that assumes that the solution can be described by the sum of amplitude function multiplied by shape functions of modes. These shape functions can be computed by solving a _-modes problems. The modal method has a great interest when the distribution of the power cannot be well approximated by only one shape function, mainly, when local perturbations are applied during the transient. Usually, the shape functions of the modal methods are updated for the time-dependent equations with a constant time-step size to obtain accurate results. In this work, we propose a modal methodology with an adaptive control time-step to update the eigenfunctions associated with the modes. This algorithm improves efficiency because of time is not spent solving the systems to a level of accuracy beyond relevance and reduces the step size if they detect a numerical instability. Step size controllers require an error estimation. Different error estimations are considered and analyzed in a benchmark problem with a out of phase local perturbation.

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