An important aspect of modeling a heat pipe involves simulating the processes within the porous structure of the wick. Understanding the transport dynamics at the liquid-vapor interface within a pore and its wetting dynamics is essential for accurately predicting the performance of heat pipes under various operating conditions and for assessing capillary dry-out limitations. For high-order simulations, we employ the eXtended Discontinuous Galerkin (XDG) method. During simulation, singularities can arise due to the appearance of the three-phase contact line. To address this challenge and enhance the stability of our numerical method, we introduce a parameterized level-set method for interface modeling. This method involves using a level-set evolution equation to describe the interface's movement and defining the level-set function based on several time-dependent parameters. Furthermore, we assume that the interface retains its parametric shape at each time step, with only the time-dependent parameters changing over time. In our research, the results obtained from the parameterized level-set method were compared with analytical solutions, and they demonstrated good agreement. To understand the impact of varying interface shapes and the rotation of a heat pipe on its efficiency, which is intended for our specific application, we performed calculations varying the interface shape parameters and the centrifugal force.