恒温边界热源一维融化问题的数值模拟

Numerical Simulation of One-dimensional Melting Problem with Constant Heat Source Boundary Condition

为了研究恒温边界热源对固体融化的影响,构建了定空间步长和定时间步长两种数值方法,研究了固体在融化过程中移动界面位置的运动规律及相变区域内温度场的变化,并将两种数值方法的模拟结果与该问题的精确解进行了对比.数值模拟结果表明相变过程中移动界面的运动受Stefan数影响较大,而相变区域内的温度场则呈现线性递减的变化趋势.此外,两种数值方法的模拟结果都具有较高的精度,与精确解吻合得非常好,说明所构造的两种数值方法都是可行的,这为固体融化问题的求解提供了参考.

In order to investigate the influences upon solid melting process caused by constant heat source boundary condition,the fixed space？step method and the fixed time？step method are constructed. The evolution of moving boundary and the temperature distribution in the phase change process are studied. The simulation results of two numerical methods are compared with the exact results. The numerical simulations show that the evolutions of moving boundary in the phase change process are influenced significantly by Stefan numbers and the temperature distributions in the phase change zone show linear decreasing trends. Moreover,the simulation results of two numerical methods have high precision and also there is a good agreement between the simulation results and the exact results ,which indicate that the two numerical methods constructed are feasible. Therefore,these researches can provide a reference for solving the solid melting problem.