In this paper, a summarization of our works in the fields of liquid-solid phase change moving interface problems is presented. Both boundary element methods to analyze these problems — the dual reciprocity boundary element method and Green function boundary element method are developed. The methods are used to analyze the thawing and freezing characters in the microgravity heat pipes. It includes: (1) analysis of the thawing startup characters in the monogroove heat pipe; (2) analysis of the freezing and thawing characters in the condenser of capillary pumped loop. A verifying experiment has also been made.