An Arbitrary-Lagrangian-Eulerian based numerical method is proposed to study the phase change bubble under the effect of noncondensable gas (NCG). In order to validate the underlying mathematical model, benchmark tests, including the bubble growth in quiescent superheated liquid and the condensation of rising bubble with NCG, are conducted. The numerical results by the phase change model, in which the mass transfer rate is directly determined by interfacial heat flux, is found to agree fairly well with analytical results, and the calculation of fluid flow and heat transfer by the present numerical approach is reasonable. Moreover, the numerical results of free rising bubble condensation with NCG are found to present good agreement with the experimental data on the evolution of bubble size, and the mass balance of the NCGs is proved to be achieved by the model. Finally, the subcooled boiling with NCG on a biphilic surface is numerically investigated, and the bubble behavior and internal distribution of the NCG are studied in detail. In the presence of NCG, the bubbles can even depart from the walls that are negatively superh yeated. The bubble keeps the bowl-shape for a long time before necking, which is consistent with the experimental observations. The contact line is found to stay at the boundary between the hydrophilic and hydrophobic surfaces. The results also show that the local accumulation of the NCG near the bubble surface decreases the local apparent saturation temperature and inhibits the condensation, and the growth and departure of bubbles is thus promoted. In addition, the amount of NCG in the bubble is found to determine whether the bubble in the subcooled boiling is detached or not. (C) 2019 Elsevier Ltd. All rights reserved.