For the numerical solution of neutron transport equations, both the positivity-preserving property and speeding up the iterative convergence are important and challenging issues. In this work, the combination of the synthetic acceleration method and a positivity-preserving scheme are derived and analyzed. For the neutron transport and the equations, we discretize them by the linear discontinuous differencing scheme and apply linear scaling limiter to obtain the non-negative solution. The limiter is simple to implement. Numerical results for solving optically thick problems verify the efficiency of the proposed schemes.

中文翻译：

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[公式省略]求解中子输运方程的合成加速和保正方案


对于中子输运方程的数值求解，保正性和加速迭代收敛都是重要且具有挑战性的问题。在这项工作中，推导并分析了综合加速方法和正性保留方案的结合。对于中子输运和方程，我们通过线性不连续差分格式将它们离散化，并应用线性标度限制器来获得非负解。限制器实现起来很简单。解决光学厚问题的数值结果验证了所提出方案的效率。