论文部分内容阅读
针对一维、稳态且含内热源的导热型微分方程,分别采用区域离散方法 A、B划分网格,然后采用Taylor展开法进行数值求解。计算结果表明:导热微分方程中边界节点采用二阶截差展开得到的离散方程,其推导过程比采用一阶截差展开复杂,尤其在计算节点间距不等(区域离散方法 B)的情况下更是如此,但其数值求解精度能够得到大幅提高,因此在实际采用Taylor展开法进行数值求解过程中推荐采用区域离散方法 B,且边界节点离散方程采用二阶截差展开。
For the one-dimensional, steady-state and heat-conducting differential equations with internal heat source, the regional discrete methods A and B are respectively used to divide the mesh and the Taylor expansion method is used to solve the numerical problem. The results show that the boundary nodes of the differential thermal conductivity equation adopt the discrete equation with the second-order truncated expansion, and the derivation process is more complicated than the first-order truncated expansion. Especially when the distance between the calculated nodes is different (the regional discrete method B) However, the accuracy of numerical solution can be greatly improved. Therefore, the regional discrete method B is recommended in the actual numerical solution using the Taylor expansion method, and the discrete equation of the boundary nodes is expanded by the second-order truncation.