Gauss-Seidel based acceleration method for solving the CRAM burnup equations

BackgroundThe reactor burnup calculation is crucial for the safe operation and fuel management of nuclear power plants. In recent years, the Chebyshev Rational Approximation Method (CRAM) has become a primary approach for solving burnup equations. When solving the burnup equations using the CRAM, the Sparse Gaussian Elimination (SGE) method is usually used for complex matrix calculation, but the improvement of computational efficiency is limited.PurposeThis study aims to develop a Gauss-Seidel (GS)-based acceleration method for solving the CRAM burnup equations to enhance the computational efficiency of the burnup equation solver.MethodsFirstly, based on the self-developed burnup calculation code AMAC, an acceleration method for solving CRAM burnup equations was developed on the basis of the GS method. Then, three burnup databases (containing 71, 221, and 1 487 nuclides) were utilized to analyze the computational accuracy and efficiency of a light-water reactor benchmark, and the results of the SGE and GS methods were compared for evaluating computational accuracy, thereby demonstrating the precision of the GS method. Subsequently, detailed analyses of the computational results of the Partial Fraction Decomposition (PFD) and Incomplete Partial Fractions (IPF) formulations based on the GS method were conducted with the Transmutation Trajectory Analysis (TTA) as the reference solution. Finally, a comparative analysis of the computational efficiency of the SGE and GS methods was performed.ResultsThe computational results show that the numerical precision of GS method is comparable for solving IPF and PFD burnup equations under different scale burnup databases. For the calculation of short-lived nuclides, the calculation accuracy of IPF is better than that of PFD. In terms of efficiency, the GS method significantly surpasses SGE method, achieving up to 80.17% acceleration across the three databases.ConclusionsResults of this study recommend the adoption of the GS-accelerated IPF formalism for practical burnup calculations to effectively balance computational accuracy and efficiency.