We developed a numerical solver to study the gas-liquid multiphase flow in the ELIPSE process developed at CEA Marcoule. The numerical strategy used to simulate its dynamics is particularly challenging because of the multi-scale nature of the flow, which involves both large gas pockets, formed during the injection of a submersed turbulent gas jet in a liquid flow, and small dispersed bubbles resulting from the breakup of these large-scale interfaces. To this purpose, the Volume Of Fluid method is coupled to a Lagrangian tracking of the emerging bubbles, by using an Adaptative Mesh Refinement strategy with a criterion of size to convert the smaller bubbles into Lagrangian objects. An LES model is used to describe the turbulent flow. By this way, we constructed the flow regime map as a function of the operating conditions of the reactor. Moreover, the heat balance is solved, and the numerical method is adapted to account for gas-liquid phase change occurring in the process. The whole simulation model allows investigating the influence of heat transfer on the flow features and gas distribution in the liquid bath.