A new Parallel Non-Dimensional Lattice Boltzmann Method (P-NDLBM) is developed to dramatically speed up the computation of transient fluid flow and heat transfer problems with larger grid numbers. The present P-NDLBM code using Message Passing Interface (MPI) was complied in Fortran, and validated by comparison to previous experimental and single core computational studies. The time cost of simulation of a natural convection problem with equal mesh size is compared for CPU numbers varies from 1 to 64, which shows the efficiency of the present P-NDLBM. Comparative studies of five models of solar collectors have been simulated by the P-NDLBM to obtain the effects of the encapsulated phase change material tubes. Also the charging and discharging procedures have been compared. The transient averaged temperature, PCM porosity and energy ratio are presented. Transient isotherms and streamlines with porosity have been clearly shown for domains both outside and inside PCM tubes. The performance enhancement because of the introduce of the PCM tubes has been presented and the effect due to distribution of the PCM tubes is also discussed. This method is also expected to be useful for further optimal design of practical complex geometry solar thermal collectors.