基于卷积型变分原理的半解析法及其在热传导中的应用(英)

Semianalytic Approach Based on Convolution-Type Variational Principle and Its Applications to Heat Transfer

本文基于卷积型变分原理提出了瞬态热传导问题的半解析法．该方法在空间域内作有限元离散，在时间上用级数表示．既吸取了现有求解瞬态问题方法的优点，又克服了其缺陷．一维和二维算例结果表明．该方法是求解热传导问题的一种新型、有效的方法．

In this article a new method of solving the transient heat transfer problems is developed that is based on convolution-type variational principle, where finite-element discretization in the space domain and series representation in the time domain are considered. This approach can overcome the shortcomings of existing methods and combine the advantages of those methods for solving transient problems. The examples show that the new method is one of the most effective method of obtaining solutions for 1D and 2D transient heat transfer problems.