Nuclear Reactor Core Simulation Red-Black Ordering
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Solution Overview
Problem
Current methods for modeling nuclear reactor cores are computationally inefficient due to sensitivity to the relaxation factor in the Successive Over-Relaxation (SOR) scheme and degrade in performance with parallelization, making it difficult to achieve robust and efficient core simulations.
Innovation Solution
The method involves partitioning the reactor core into red and black cubes, using a red-black ordering and a Bi-Conjugate Gradient Stabilized (Bi-CGStab) procedure with a checkerboard-preconditioned approach, which allows for efficient iterative solving of linear systems and eigensystems, reducing the need for manual parameter tuning and improving parallelization efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If Successive Over-Relaxation (SOR) scheme is used to accelerate convergence, then convergence speed is improved, but computational performance becomes highly sensitive to relaxation factor parameter
Solution Approach 1:
The method uses the existing matrix structure (checkerboard pattern from red-black ordering) to automatically determine optimal relaxation factors for different regions, eliminating the need for manual parameter tuning. Each processor independently determines its optimal parameter based on local cube characteristics.
Solution Approach 2:
The invention changes the relaxation factor parameter dynamically based on the checkerboard position (red vs black cubes) and processor assignment. Instead of using a fixed global relaxation factor, the method applies different factors ω_red and ω_black to different cube types, optimizing convergence for each region.
2Ease of manufacture
If lexicographical ordering is used for cube numbering, then implementation simplicity is maintained, but computational efficiency degrades with parallelization
Solution Approach 1:
The method segments the cube set into two independent subsets (red cubes and black cubes) that can be processed separately. This segmentation allows processors to work on non-adjacent cubes simultaneously without conflict, enabling efficient parallelization while maintaining the simplicity of the ordering scheme.
Solution Approach 2:
The invention introduces a new dimension to the ordering by adding color classification (red/black) to the traditional lexicographical ordering. This creates a two-level ordering system where cubes are first classified by color, then numbered within each color group, enabling parallel processing while maintaining implementation simplicity.
3Ease of operation
If fixed relaxation factor is used for different computational cases, then ease of operation is improved, but computational robustness deteriorates
Solution Approach 1:
The method automatically adapts the relaxation factor parameters based on the specific computational case and matrix structure. By calculating optimal ω values from the matrix properties themselves, the system maintains both ease of operation (no manual tuning needed) and computational robustness (optimized for each case).
Data Source
AI summary
The method comprises the steps of: partitioning the core in cubes to constitute nodes of a grid for computer implemented calculation, splitting the cubes into a first category and a second category, each cube of the first category being adjacent only to cubes from the second category so that the first category and second category of cubes constitute a checkerboard-like pattern, ordering the cubes of the first category and then the cubes of the second category, calculating neutron flux and/or thermohydraulics parameters by using an iterative solving procedure of at least one linear system and/or an eigensystem, the components of an iterant of the linear system and/or the eigensystem constituting the neutron flux and/or thermohydraulics parameters to be calculated, wherein, during the iterative solving procedure, calculations are conducted on the cubes of the first category then on the cubes of the second category.