The goal of this paper is to investigate the aerodynamic and aerothermodynamic behaviour of the Schiaparelli capsule after the deployment of the supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. Large-Eddy Simulations of compressible flows have been performed over the capsule and the flexible DGB parachute to analyse the behaviour of the turbulent wake behind the capsule and its interaction with the parachute flow-field. The simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. These simulations have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. This nonlinear turbulence flowfield explains the non-axisymmetric behaviour around and behind the parachute that caused the uncontrolled capsule oscillation and the mission failure.