The underexpanded jets are present in many processes such as rocket propulsion, mass spectrometry, fuel injection, as well as in the process called rapid expansion of supercritical solutions (RESS). In the RESS process a supercritical solution flows through a capillary nozzle until an expansion chamber where the strong changes in the thermodynamic properties of the solvent are used to encapsulate the solute in very fine particles. The research project was focused on the hydrodynamic modeling of an hypersonic carbon dioxide jet produced in the context of the RESS process. The mathematical modeling of the jet was developed using the set of the compressible Navier-Stokes equations along with the generalized Bender equation of state. This set of PDE was solved using an adaptive discontinuous Galerkin discretization for space and the exponential Rosenbrock-Euler method for the time integration. The numerical solver was implemented in C++ using several libraries such as deal.ii and Sacado-Trilinos.