The compressibility of high-speed flows introduces density and energy variation in the descrip- tion of the fluid motion studied in the Computational Fluid Dynamics (CFD) framework. The goal of this thesis is the implementation of a finite element solution for the compressible Navier-Stokes equations, which describe accurately the behavior of continuous isotropic fluids. The Galerkin approximation used for the discretization is unstable for convective dominant problems. Including the Variational Multi-Scale (VMS) formulation the stabilization is achieved. Additionally, an isotropic shock capturing technique is implemented to stabilize locally the solution in transonic and supersonic regimes. The technique is based on the increase of the numerical diffusion where shock waves occur. The compressible Navier-Stokes element has been included into Kratos Multiphysics, an open- source software for the numerical modeling, written in C++ and Python. The implemented solver is verified using the Method of Manufactured Solutions. The validation for two- and three-dimensional problems is performed comparing the numerical results of the inviscid shock reflection and the Sod shock tube with analytical solutions. Accu- rate results are also obtained testing the transonic flow over a Naca 0012 against the AGARD experimental data.     «

The compressibility of high-speed flows introduces density and energy variation in the descrip- tion of the fluid motion studied in the Computational Fluid Dynamics (CFD) framework. The goal of this thesis is the implementation of a finite element solution for the compressible Navier-Stokes equations, which describe accurately the behavior of continuous isotropic fluids. The Galerkin approximation used for the discretization is unstable for convective dominant problems. Including the Variat...     »