求解瞬时温度场的有限元显式算法

在一公共节点为中心的各单元中,对于线性形函数,实际计算和数字实验表明,温度在单元各节点上的时间导数用它在中心节点上的时间导数表示是可取和合理的。由此可在对微分方程用有限元法进行空间离散的基础上得到单个节点温度的时间导数与其周围节点温度的关系,建立温度场的显式计算格式。它具有计算简捷的特点。用最大值原理对稳定性的分析导出了与稳式算法类似的稳定性条件。

A Finite Element Explicit Algorithm for Solving the Temporal Temperature Fields

Practical calculations and numerical experiments in this paper have shown that in elements relating to a common node it is acceptable and reasonable for derivaties of temperature with respect to time on nodes of those elements to be presented with one on common node,if linear interpolation shape function is taken.The relation between the derivative of temperature to time on a certain node and the temperature on other nodes around that node may therefore be established after discretization of the differential equation is made in space by the finite element method.Then an explicit scheme for calculating the temperature fields may be constructed.The obtained algebraic equations,being simple and the procedure being straight will be its two tangible advantages and its calculating will,therefore,be fast.The stability analysis by the maximum principle,as in the example quoted,proves that the stability condition is similar to that in implicit algorithms.