Nuclear Reactor Core Modeling via Spectral Decomposition
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Solution Overview
Problem
Current methods for modeling nuclear reactor cores face challenges in achieving accurate and efficient neutron flux calculations due to slow convergence and increased computational efforts, particularly with Coarse Mesh Rebalancing procedures that depend on the proximity of the coarse mesh level to the full-core diffusion level.
Innovation Solution
A computer-implemented method for modeling nuclear reactor cores that partitions the core into cubes for grid-based calculations, using an iterative solving procedure to calculate neutron flux by varying a control parameter through a perturbed interface current equation, driving the neutron eigenvalue towards a specific value, and employing sparse eigensystem conditioning and spectral restriction to improve convergence accuracy and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Coarse Mesh Rebalancing procedures are used to accelerate eigensystem solving, then computational efficiency is improved, but convergence accuracy deteriorates and computational robustness worsens due to dependence on mesh level proximity
Solution Approach 1:
The patent transforms the neutron flux representation from a standard nodal expansion into a spectral decomposition form, changing the mathematical parameters used in the calculation. This spectral representation with carefully selected basis functions enables faster convergence while maintaining accuracy, resolving the contradiction between computational efficiency and convergence accuracy.
Solution Approach 2:
The patent introduces adaptive spectral coefficients that dynamically adjust during the iterative solving process. These coefficients are optimized at each iteration step to accelerate convergence toward the fundamental eigenvalue, making the computational method both efficient and accurate by adapting to the evolving solution state.
2Reliability
If standard iterative solving procedures are used for the eigensystem, then computational robustness is maintained, but computational efficiency deteriorates due to slow convergence
Solution Approach 1:
The patent introduces spectral basis functions as intermediary mathematical tools that mediate between the standard nodal representation and the solution. These spectral functions act as a bridge that accelerates convergence by providing a more effective mathematical framework, thereby improving computational efficiency while maintaining the robustness of iterative solving.
3Speed
If the coarse mesh level is kept close to the full-core diffusion level for CMR acceleration, then convergence speed is improved, but adaptability deteriorates and robustness worsens
Solution Approach 1:
The patent develops a spectral representation method that serves multiple functions: it accelerates convergence for the fundamental eigenvalue, maintains accuracy for higher eigenvalues, and adapts to different mesh configurations. This universal approach eliminates the need to optimize mesh levels specifically for CMR, providing both speed and adaptability simultaneously.
Data Source
AI summary
A computer implemented method for modelizing a nuclear reactor core, including the steps of: partitioning the core in cubes to constitute nodes of a grid for computer implemented calculation, calculating neutron flux by using an iterative solving procedure of at least one eigensystem, the components of an iterant of the eigensystem corresponding either to a neutron flux, to a neutron outcurrent or to a neutron incurrent, for a respective cube to be calculated.A control parameter is varied to impact a neutron eigenvalue μ through a perturbed interface current equation and drive the neutron eigenvalue μ towards 1.