Computational fluid dynamics is nowadays one of the pillars of modern aircraft design, just as important as experimental wind tunnel testing. Very ambitious goals in regards to performance, efficiency and sustainability are being asked of the aviation industry, the kind that war
...

Computational fluid dynamics is nowadays one of the pillars of modern aircraft design, just as important as experimental wind tunnel testing. Very ambitious goals in regards to performance, efficiency and sustainability are being asked of the aviation industry, the kind that warrant a virtual exploration of the edges of the flight envelope. High order has come to be regarded as a necessary ingredient to achieve breakthrough advances in this direction. So much so, in fact, that the major aircraft manufacturers, governmental aerospace research agencies and top universities worldwide have been acting in coordination to increase the technology readiness level of these approaches, for the last ten years. In this work, I study in significant detail the one aspect that makes high-order methods ideal candidates for enabling the use of more advanced turbulence models in industry: the cost-efficiency of their discretization—they offer minimal amounts of dispersion and dissipation errors, for a given number of degrees of freedom. I consider three research objects: discontinuous Galerkin spectral method (DGSEM), flux reconstruction (FR) and a novel B-spline-based discontinuous Galerkin formulation stabilized via algebraic flux correction (DGIGA-AFC), and characterize their order of accuracy, linear and nonlinear stability characteristics, as well as dispersion and dissipation errors as a function of wavenumber. Afterwards, I experimentally investigate their relative suitability towards scale-resolving simulation of compressible and turbulent flows, by solving a number of simple test cases of increasing difficulty (linear advection, inviscid Burgers and Euler equations; all in 1D) using a purpose-made MATLAB implementation. The proposed isogeometric method (DGIGA) has been found to be at least as viable as the other two, a priori, for the resolution of high-speed turbulent flows. Moreover, I have found that low dispersion and dissipation need not always be associated to high order, but to a high number of degrees of freedom per patch instead; these two coincide in the more conventional schemes, yet not necessarily in DGIGA. As a nonlinear stabilization mechanism, however, the proposed combination of DGIGA with AFC has turned out to be inferior to existing limiters.