带相变瞬态温度场问题的扩展有限元解析

带相变瞬态传热问题是寒区工程多场耦合问题求解的关键.在剖析常规有限元法在求解带相变瞬态温度场问题的不足的基础上，结合冻土冻融温度变化的特点，提出采用扩展有限元法求解冻土工程带相变瞬态传热问题的新方法，以四边形单元为例推导了冻土工程温度场的求解格式，详细剖析了瞬态传热过程中移动界面水平集函数的构造、单元刚度矩阵的形成及高斯积分的求解.据此编写了相应的扩展有限元程序，通过经典Stefan问题全面验证了程序的正确性与合理性.

Extended finite element method analysis for the transient temperature field with phase change

Transient heat transfer with phase change is the key to the solving of the multi-field coupling problems in cold regions.The freezing process of frozen soil can be divided into four stages based on the measured freez-ing curves in Changchun.Analyzing the shortage of the traditional finite element method in solving the phase change problem and the characteristic of frozen soil′s freezing process,the extended finite element method (XFEM)was proposed for solving the transient heat transfer problem with phase change for permafrost engineer-ing.The XFEM interpolating function and solving format of temperature field with phase change was derived that taking quadrilateral element as an example.Based on the study of the constructing and solving of the level set function,building of the stiffness matrix and subdividing of the elements,a XFEM program for the transient heat transfer problem with phase change was proposed in this paper which has been verified by classical Stefan prob-lem.