瞬态热传导问题的修正变分原理及其数值算法

Modified Variation Principle and Numerical Algorithm of Transient Problem of Heat Conduction

本文采用拉格朗日乘子将本征边界条件引入到瞬态热传导问题的泛函方程,通过变分原理得到了其修正泛函.采用Galerkin无网格法在空间域内进行离散,得到瞬态热传导问题的半离散方程;在时间域上通过与Romberg积分相结合的精细积分法求解,并且推导了瞬态热传导方程中精细积分的普遍适应的公式,结合数值算例对方法的有效性和精确性进行了验证.

In this paper,the essential boundary conditions are introduced to the functional of transient problem of heat conduction with Lagrange multiplier,and the modified functional equation is constructed by the variation principle.The semi-discretization equation is obtained by Galerkin element free method in spatial domain,and is solved by time precision integration method and Romberg integration in the time domain.Also,a uniform solution is pressented.The numerical results indicate that the algorithm is effective and accurate.