模拟相变问题的精细积分边界元法

将精细积分边界元法和界面追踪法相结合求解相变问题。因为边界元法只需要将待求解空间域的边界离散,方便连续追踪移动界面位置和重构网格,所以边界元法适合应用于移动边界问题的模拟。首先,利用精细积分边界元法在固相区域和液相区域分别求解相应的瞬态热传导控制方程,从而求得温度场和边界热流密度。然后,根据固-液相变界面上的能量平衡方程,利用热流密度求得相变界面的移动速度,再采用界面追踪法预测移动相变界面的位置变化。最后,给出了几个数值算例,并通过与参考解的对比验证本文方法的准确性。

Simulation of phase change problems by precise integration boundary element method

The precise integration boundary element method is combined with the front tracking method to simulate the phase change problems in this paper.One of the merits for the boundary element method is that only the boundary needs to be discretized,so it is easy for the implementation of grid deforming and remeshing.Firstly,the governing equations of heat conduction are solved by the precise integration boundary element method in the solid phase domain and the liquid phase domain respectively,and the moving velocity of the solid-liquid interface can be obtained by the heat flux on the interface and the energy balance equation.Then,an iterative algorithm of the front tracking method is adopted to track the moving interface.Finally,several numerical examples are presented to verify the validity and accuracy of the proposed method.