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Modal methods for the neutron diffusion equation using different spatial modes
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DOI：10.1016/j.pnucene.2019.03.040.png)
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Abstract
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The behaviour of the neutrons inside a nuclear reactor core can be modelled by using the time dependent neutron diffusion equation. Different time schemes have been used to integrate this equation. One possibility is to use a modal method, which is based on the expansion of the neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the neutron diffusion equation such as the lambda, alpha and gamma-modes. In this work, the lambda, the alpha and the gamma-modes have been used to develop different modal kinetics equations, using a high order finite element method for the spatial discretization of the neutron diffusion equation. The performance of the different modal kinetic equations has been tested and compared using two 3D transient benchmark problems.
Keywords:
Modal method
Finite element method
Time dependent neutron diffusion equation
Spatial Modes
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