Shock-fitting techniques on 2D/3D unstructured and structured grids: algorithmic developments and advanced applications

Over the last decades the simulations of compressible flows featuring shocks have been one of the major drivers for developing new computational algorithms and tools able to compute also complex flow configurations. Nowadays, Computational fluid dynamics (CFD) solvers are mainly based on shock capturing methods, which rely on the integral form of the governing equations and can compute all type of flows, including those with shocks, using the same discretization at all grid points. Consequently, these methods can be implemented with ease and provide physically meaningful solutions also for complex flow configurations, features particularly attractive for CFD community. Although shock capturing methods have been the subject of development and innovations for more than 40 years, they are plagued by several numerical problems due to the shocks capture process, such as discontinuities finite-width, numerical instabilities and reduction of accuracy order in the shock downstream region, which are still unsolved and probably will never find a solution. For this reason, there is a renewed interest in shock-fitting techniques: in particular, these methods explicitly identify the discontinuities within the flow field and compute them by enforcing the Rankine-Hugoniot jump relations. Because of this modelling, shocks are represented by zero thickness discontinuities, so that significant advantages can be gained in terms of solution quality and accuracy improvements. Furthermore, this class of methods is immune to the numerical problems linked to shock capture process. Following this research line, the presented Thesis proposes new developments and advanced applications of shock-fitting techniques, which prove that these methods are an effective option regarding shock capturing ones in simulating flows with shocks, able to provide also a better understanding of all the phenomena linked to shock waves.