层合结构瞬态热传导方程的一种精细解法

摘要

提出了层合结构瞬态热传导方程的一种精细解法,该方法适用于单层或者多层介质的情况.首先将结构的瞬态热传导方程沿空间方向均匀(单层介质)或者分段均匀(多层介质)离散,转化为关于时间的常微分初值问题,然后将离散后的拉普拉斯差分算子由块三角矩阵转化为块对角形式,结合已有的精细积分算法,建立了求解层合结构瞬态热传导问题的一种有效方法.该方法具有良好的精度,还可以无条件地满足算法的稳定性要求,算例表明了这方法的有效性.%An efficient algorithm of two-dimensional transient heat conduction equation is presented for laminate structure, including single-media and multi-media. Firstly the transient heat conduction equation is discretized uniformly (for single-media) or uniformly on each media (for multi-media) along the space axis and then changed into ordinary differential initial value problem (ODIVP) about the time t. The Laplace differential operator is discrete into block tri-diagonal matrix which is changed into block diagonal form. The precise time integration ( PTI) is employed in the solution of the ordinary differential initial value problem which is effective for the transient heat conduction problem of laminate structure. The numerical examples are presented to demonstrate the precision, numerical stability and applicability of the proposed method.