A novel isogeometric boundary element approach for solving phase change problems with the level set method

In this study a new algorithm is proposed for numerically solving phase change problems. The algorithm (PTEIGBEM) integrates the precise time domain expanding method (PTE) and the isogeometric boundary element method (IGBEM). The governing equations are transformed into recursive form by expanding the variables within the time period. The domain integral is transformed into boundary integral by the dual reciprocity method (DRM). An adaptive checking scheme is used to determine the number of expanding items required for a time period. In addition, the level set method (LSM) is used to capture the trajectory of the front separating the solid and liquid phases. Several classical examples are given to demonstrate the accuracy and robustness of the algorithm.