淬冷过程三维温度场有限元模拟数值振荡问题的研究

用作者编写的三维有限元程序对淬冷过程温度场进行了模拟计算，并与解析解（分离变量法）进行了比较。为了解决数值振荡问题，采用了局部网格细化、动态时间步长和集中热容矩阵等方法。通过模拟结果与解析解的比较可以看出，在时间步长选择合适的情况下，集中热容矩阵能够很好地解决数值振荡问题；如果不进行集中热容矩阵，无论是细化网格还是减小时间步长，其解决数值振荡问题的效果都不好。

Numerical Oscillation in FEM Based Simulation of 3D Temperature Field for Quenching Processes

The three dimensional temperature field of quenching process was simulated with the finite element program developed by the author.The methods of local mesh refined,dynamic time step and lumped heat capacity matrix were introduced to resolve the numerical oscillation problem.The results show that the simulation results fit the theoretic results(by separate variable method)very well when the heat capacity matrix is lumped with appropriate time step.However,if the heat capacity matrix is not lumped,the numerical oscillation problem can not to be resolved even though by refining the local mesh or by decreasing the time step.