A new mesoscopic scale Parallel Non-Dimensional Lattice Boltzmann Method (P-NDLBM) is developed to dramatically speed up the computation of transient fluid flow and heat transfer problems. The P-NDLBM code using message passing interface (MPI) was compiled in Fortran. The model is presented in dimensionless form to simplify application to a broad range of problems. The effective domain decomposition, data transfer between CPUs, and various boundary conditions based on the P-NDLBM are presented. The code is validated by comparison to prior experimental and single CPU computational studies of cavity flow and the Rayleigh–Bénard problem. The time costs of simulations with equal mesh size are compared for CPU numbers from 1 to 64 to show the effectiveness of the approach. To illustrate the utility of the code, simulations of the transient temperature and fluid velocity during charging and discharging of an integral collector storage solar system are presented. The modeled system has encapsulated phase change embedded in the water-filled enclosure. The results illustrate the capability of the code to capture the phase transition within the encapsulated phase change material as well as the details of the overall flow structure and temperature field.