Mathematics

High-order methods for fluid dynamics represent a trending topic in the Computational Fluid Dynamics (CFD) community, gaining more and more popularity in both academia and industry. Their computational efficiency and geometric flexibility make them promising candidates as building blocks for the next generation of commercial solvers. Today's talk will be focused on the use of high-order spectral element methods for the simulation of compressible turbulent flows. Under such conditions, three main complex modelling challenges can be identified: the development of low dissipative shock-capturing techniques, the quantification of numerical dispersion/diffusion of spatial discretizations and the modelization of compressibility effects in turbulent flows. A good equilibrium between these three aspects is of fundamental importance for the overall success of numerical simulations. The first part of the talk will be focused on a low dissipative shock-capturing technique based on an artificial bulk viscosity. In the second part, classical techniques to estimate numerical dispersion and diffusion of high-order methods will be presented and discussed. Finally, a series of fully-turbulent compressible flows will be considered. In these simulations shock-waves, turbulence and numerical spurious artifacts will be simultaneously involved, strongly interacting one another. In particular, as a final, inclusive, test case, a Direct Numerical Simulation of a compression/expansion ramp will be used to investigate kinetic energy transfers in presence of non-negligible compressibility effects.