时域径向积分边界元法在平面单相凝固问题中的应用

该文将时域精细积分边界元方法与界面追踪法相结合，给出平面单相凝固热传导问题的一个有效数值分析方法。首先，利用稳态热传导问题的基本解和径向积分法给出瞬态传热问题的边界积分方程，并采用精细积分方法求解离散的微分方程组，获得相变界面的热流密度。然后应用相变界面上的能量守恒方程，采用界面追踪法来预测相变边界的移动位置，从而给出相关问题数值模拟的结果。最后，为验证该文方法的有效性，给出两个数值算例并与解析解进行了对比。结果表明，该文方法具有较高的求解精度，是求解相变热传导问题的一种有效数值方法。

THE APPLICATION OF THE TIME DOMAIN RADIAL INTEGRAL BOUNDARY ELEMENT METHOD IN 2D ONE-PHASE SOLIDIFICATION

A combined approach of the precise integration boundary element method and the front-tracking method is presented for thermal conduction problems with one-phase solidification. Firstly, the boundary integral equation of transient thermal conduction is given by using the fundamental solution of steady-state thermal conduction problems and radial integration method. The precise integration method is applied to solve the discrete differential equations for obtaining the heat flux density of the moving boundary. Then the energy conservation equation of the moving boundary and the front-tracking method are applied to predict the position of the moving boundary, and the results of numerical simulations are obtained. To validate the proposed method, two typical examples are given and compared with the analytical solutions. The results show that the proposed method has a high accuracy and is an effective numerical method for solving thermal conduction problems with phase solidification.