核燃料导热方程数值求解算法研究

Study on Numerical Solving Algorithm of Nuclear Fuel Thermal Conductivity Equation

针对核燃料子通道分析方法中导热方程矩阵维度较大的问题,引入多种三对角矩阵数值求解方案,研究不同矩阵维度下数值求解方法的适用性。通过推导核燃料导热方程,对方程的特点进行分析,引入条件数判别法对矩阵的病态程度进行量化,使用列选主元三角分解法、超松弛迭代法和共轭梯度法对不同维度大型稀疏试算矩阵进行求解,比对各数值求解方法的残差平方和,并在一定精度下比对迭代求解方法的收敛步数。在综合考虑计算精确度和速度后,给出不同条件下核燃料导热方程的数值求解方案。

In view of the large matrix dimensions of the thermal conductivity equation in the nuclear fuel subchannel analysis method,several numerical solutions of tridiagonal matrix are introduced to study the applicability of numerical solutions under different matrix dimensions.By derivation of the nuclear fuel thermal conductivity equation,the characteristics of the equation were analyzed,the condition number discriminant method was introduced to quantify the pathological degree of the matrix,the column selection principal element trigonometric decomposition method,the overrelaxation iterative method and the conjugate gradient method were used to solve the large sparse trial matrix of different dimensions,and the residual sum of squares of each numerical solution method was compared.The convergence steps of the iterative solution are compared under certain precision.After considering the calculation accuracy and speed,numerical solutions of nuclear fuel thermal conductivity equations under different conditions are given.