扩散临界计算中的多重迭代优化技术

Multi-level Iteration Optimization for Diffusive Critical Calculation

核反应堆堆芯中子扩散计算中一般存在至少3重迭代：裂变源迭代、多群散射源迭代和群内迭代。为避免相邻两重迭代之间产生的内层迭代收敛太强会引入多余计算量、收敛太弱会使外层迭代收敛性变差甚至不收敛的问题，本文针对采用带Gauss—Seidel左预处理的多群GMRES算法的变分节块法，设计并验证了一种对大多数问题均适用的多重迭代优化技术，其优化设置多群迭代和群内迭代的收敛准则的基本思想是：相应内层迭代收敛误差限正比于相应外层迭代的误差衰减率。数值计算基于商用压水堆和钠冷快堆选取的两个有代表性的堆芯算例进行，相应的结果表明：该多重迭代优化技术可对多群迭代加速约1～2倍，对群内迭代加速约5～21倍。

In nuclear reactor core neutron diffusion calculation, there are usually at least three levels of iterations, namely the fission source iteration, the multi-group scattering source iteration and the within-group iteration. Unnecessary calculations occur if the inner iterations are converged extremely tight. But the convergence of the outer iteration may be affected if the inner ones are converged insufficiently tight. Thus, a common scheme suit for most of the problems was proposed in this work to automatically find the optimized settings. The basic idea is to optimize the relative error tolerance of the inner iteration based on the corresponding convergence rate of the outer iteration. Numerical results of a typical thermal neutron reactor core problem and a fast neutron reactor core problem demonstrate the effectiveness of this algorithm in the variational nodal method code NODAL with the Gauss-Seidel left preconditioned multi-group GMRES algorithm. The multi-level iteration optimization scheme reduces the number of multi-group and within-group iterations respectively by a factor of about 1-2 and 5-21.