Conventional High-Performance Computing (HPC) methods for PDE equations numerical solvers are reaching their acceleration limit. 
As we move toward the exaflops supercomputing era, numerical PDE solvers parallelization reaches its saturation point in the spatial dimension and is restricted by the time domain instead. 
This restriction leads to the development of parallel-in-time methods. Various parallel-in-time methods have been developed since the year 1964. 
Well-known methods such as parareal and multigrid reduction in time (MGRIT) have been shown to provide reasonable acceleration to partial differential equations (PDE) implicit schemes. 
However, only a few have applied pure explicit schemes. This research introduces a parallel-in-time method optimized for explicit schemes. 
The proposed method constructs a multiple coarsening layer structure and solves the parareal algorithm through coarse to fine layers. 
Furthermore, the relaxation method is defined to solve across the whole time segment divided by the number of processors. 
This way improves the efficiency of parallel-in-time solvers with a limited amount of processors. 
This research conducts numerical experiments for a two-dimensional simulation of compressible viscous flow around a circular cylinder, using explicit time-marching schemes as relaxation methods. 
The research result shows that the proposed parallel-in-time method could improve the computation efficiency of explicit solvers compared to pure spatial parallelization. 
Furthermore, we are working on applying adaptive mesh refinement to extend the two-dimensional result for supersonic flow with shock wave appearances.