基于最佳一致逼近多项式的燃耗计算方法研究

本文研究了一种基于最佳一致逼近多项式（MMPA）的燃耗计算方法求解燃耗方程。相比于切比雪夫有理近似方法（CRAM）和围道积分有理近似方法（QRAM），MMPA方法只需一次矩阵求逆计算即可求解燃耗方程，且所有计算都是实数运算，具有数值稳定性好、求解效率高等优点。进一步研制了基于MMPA方法的点燃耗程序AMAC，并耦合蒙特卡罗输运程序OpenMC，采用衰变例题、固定辐照例题、OECD/NEA压水堆栅元燃耗基准题和沸水堆组件燃耗基准题进行验证，程序计算结果与实验值及各参考值吻合良好，初步验证了MMPA方法在理论和数值上的正确性和有效性。

Research of Burnup Calculation Method Based on Mini-max Polynomial Approximation

An alternative method based on the mini-max polynomial approximation (MMPA) method was studied to compute the exponential of the burnup matrix in the paper. Against Chebyshev rational approximation method (CRAM) and Quadrature-based rational approximation method (QRAM), MMPA method can solve the burnup equation with only on inverse calculation, and all computations are real arithmetic, which has the advantages of good numerical stability and high solution efficiency. Furthermore, based on MMPA method, the burnup calculation code named AMAC was developed and coupled with the Monte Carlo transport code OpenMC, which was verified by decay and fixed flux irradiation problems,a series of OECD/NEA burnup credit criticality benchmarks, including pressurized water reactor (PWR) pin-cell benchmark and boiling water reactor (BWR) assembly benchmark. The calculation results are in good agreement with the experimental values and the reference values. The correctness and effectiveness of the MMPA method in theory and numerical value are preliminarily verified.