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研究了核反应堆运行过程和燃料管理的数学描述,在时间半离散化后的每一个时间步长上,由椭圆型偏微分方程本征值问题来控制反应性,并得到了堆内中子通量分布、功率分布和核燃料辐照值分布,作为数学物理反问题。对调节临界和换料进行数学描述,并将这一全过程的数学描述,进行计算机数值模拟。在运用有限元方法求解中子扩散方程的本征值问题中,给出了一个加速收敛迭代方法,使有效增殖系数的计算时间与差分方法相比大为减少,与国际上同类问题有限元算法比较,速度也快得多。
The mathematical description of reactor operation and fuel management was studied. At each time step after the discretization of time, the reactivity was controlled by the eigenvalue problem of elliptic partial differential equations, and the in-reactor neutron flux Distribution, power distribution and nuclear fuel irradiation value distribution, as the inverse problem of mathematical physics. Mathematical description of the adjustment of the critical and refueling, and the whole process of mathematical description, computer numerical simulation. In solving the eigenvalue problem of neutron diffusion equation by using finite element method, an iterative method of accelerating convergence is given, which greatly reduces the computation time of effective multiplication coefficient compared with the difference method. Compared with the international finite element method Comparing, the speed is much faster.