In recent years, there has been growing interest in the development of reversible thermal storage systems for urban development. The present work deals with one of these systems, which consists of a fluid flow carrying microcapsules containing a phase-change material (mPCM, cf. [1]) circulating in a porous layer integrated into the urban structure. It focuses on the the melting process occurring in the fluid-driven encapsulated phase change material. The fluid equations inside and outside the capsule are solved using the lattice-Boltzmann method on a two-dimensional simulation. A collision operator based on the partial saturated method ensures the boundary conditions at the interfaces between fluid and solid phases. A second set of distribution functions on the lattice is used to solve heat transfer, while an enthalpy-based model provides a realistic solution for the phase change, by means of an enhanced multi-relaxation-time collision operator. The results are detailed and investigated in order to understand the impact of several parameters (Reynolds number of the fluid, Stefan number of the phase-change material) on the phase change kinetics. The effect of the angular velocity of the shell with respect to its content is evaluated in particular.