A high fidelity multi-physics Eulerian computational framework is presented for the simulation of supersonic parachute inflation during Mars landing. Unlike previous investigations in this area, the framework takes into account an initial folding pattern of the parachute, the flow compressibility effect on the fabric material porosity, and the interactions between supersonic fluid flows and the suspension lines. Several adaptive mesh refinement (AMR)-enabled, large edge simulation (LES)-based, simulations of a full-size disk-gap-band (DGB) parachute inflating in the low-density, low-pressure, carbon dioxide (CO2) Martian atmosphere are reported. The comparison of the drag histories and the first peak forces between the simulation results and experimental data collected during the NASA Curiosity Rovers Mars atmospheric entry shows reasonable agreements. Furthermore, a rudimentary material failure analysis is performed to provide an estimate of the safety factor for the parachute decelerator system. The proposed framework demonstrates the potential of using Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI)-based simulation tools for future supersonic parachute design.