Based on the two-dimensional/axisymmetric high-precision compressible multiphase flow computational fluid dynamics method  multi-scale simulation code  (MuSiC)-consistent, conservative, all-speed, sharp-interface method (CCASSIM), we propose a parallel area decomposition  method to deal with structural grids. According to different communication ways of boundary data on each processor, blocking and non-blocking communication algorithms are designed respectively. We also develop a MPI / OpenMP hybrid parallel optimization algorithm to reduce communication overhead. Some  numerical experiments are performed on Tianhe-2 supercomputer system with the maximum of grid cells of 1.2 × 1010 and 8 192 processors. The results show that the average parallel efficiency of the program that uses the MPI / OpenMP hybrid parallel algorithm, the pure MPI parallel algorithm with non-blocking communication, and the pure MPI parallel algorithm with blocking communication is 86%, 83% and 77% respectively. Futhermore, good scalability is also observed from the test results of the above three algorithms.