摘要
用有限元法求解热传导方程经常会得到振荡或超界的结果,这个重要问题一直没得到很好的解决。我们提出时间单调性和空间单调性的概念,推导和证明了获得合理解答的计算准则。对一维问题,推出关于△t/△x^2的上下界公式,并详细讨论了时间单调性,空间单调性及其与△t/△x^2的关系。最后把本文的计算准则与传统的特征值法作了比较。
In finite element analysis of transient temperature field due to heat conduction, it is quite notorious that the solution may very likely oscillate and/or exceed reasonable scope, which violates the natural law of heat conduction. To solve this critical problem, we first put forward the concepts of time monotony and spatial monotony, and then derive several sufficient conditions for reasonable solutions. For 1-D problems, the lower and upper bound for △t/△x2 can be derived and spatial monotony is studied. We also compare our results with those by classical eigenvalue method. Several useful conculsions are drawn finally. We have made a breakthrough in the field of numerical transient analysis.
