中文摘要：

借助空间坐标变换,把移动区域模型转化为固定区域模型,通过构造显式和隐式两种有限差分格式求解热源周期振荡条件下的一维融化问题.对所构造的两种差分格式分别研究它们的数值稳定性,比较它们的计算量和计算效率;应用这两种差分格式分别数值模拟融化过程中移动边界的运动及液态介质内温度场的分布.数值实验结果表明,这两种差分格式的数值结果吻合得非常好,而隐式差分格式的计算效率要明显优于显式差分格式.

英文摘要：

Two finite difference schemes,the explicit and implicit schemes,were established to solve the one-dimensional melting problem with periodic heat source,while the moving boundary model of the melting problem was transformed to a fixed boundary model by a simple stretching of the spatial coordinate. The numerical stabilities of the explicit and implicit schemes were studied. The computational complexity and efficiency of these two schemes were compared. Also the evolution of the moving boundary and the temperature distribution were simulated numerically by using these two finite difference schemes for the one-dimensional melting problem with periodic heat source. Numerical experiment results showed that the results obtained from these two schemes were in good agreement,but the computational efficiency of the implicit scheme was much higher than that of the explicit scheme.