论文标题
耦合热中性问题的分析解决方案和数值方法
Analytic solutions and numerical method for a coupled thermo-neutronic problem
论文作者
论文摘要
我们在这一贡献中考虑了一个简化的理想化的一维模型，在核心反应器中，将中子通量扩散方程与水的焓方程耦合，从而收集了该理想化的核心芯产生的热量。这些方程是通过焓扩散方程的依赖性依赖性的。我们提出了一种数值方法，该方法在全球范围内处理了找到其独特解决方案的耦合问题。相似地，我们使用不完整的椭圆形积分来分析中子的密度和流体中的焓。两种方法都以高精度导致了samesolution。但是，另一个数量通常用作比较结果的基准，这在很大程度上取决于用于扩散方程系数的近似值。
We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this idealized nuclear core. These equations are coupled through the dependency of thecoefficients of the diffusion equation in terms of the enthalpy. We propose a numerical method treating globally the coupled problem for finding its unique solution.Simultaneously, we use incomplete elliptic integrals to represent analytically the density of neutrons and the enthalpy in the fluid. Both methods lead to the samesolution with high accuracy. However, another quantity, generally used as a benchmark for comparing results, depends considerably on the approximation used forthe coefficients of the diffusion equation.
