This research project aims to develop a novel kind of high order gasdynamic solvers for structured meshes able to compute viscous flows with shock waves.
These solvers will be based on an approach recently developed by the PI for gasdynamic solvers for unstructured meshes that combines the shock-fitting technique with some ideas coming from embedded boundary techniques. This new shock-fitting approach breaks the existing link in the old boundary shock-fitting techniques between the topology of the computational grid and the shock position.
This connection was very limiting in the case of structured grids due to the rigid topology of the structured grids and has prevented the development of shock-fitting solvers for structured grids able to compute complex flows.
The use of this new shock-fitting approach will allow to remove these constraints and to obtain a new class of solvers much more accurate than those used today in DNS and LES simulations or in direct acoustic simulations of flows with shock waves.
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A quick analysis of the CFD articles published today shows that shock capturing methods are the only numerical techniques used in simulations of compressible non-viscous/viscous, laminar/turbulent flows. This wide spread of this class of solvers actually hides some unsolved problems. Despite more than four decades of algorithmic developments, shock-capturing schemes continue to show several numerical problems that do not find a convincing cure.
Among these, it is worth mentioning: the reduction of the order of accuracy downstream of a captured shock-wave, the generation of spurious oscillations and the carbuncle phenomenon [23,24].
Shock-fitting techniques could be a valid alternative to shock-capturing techniques, as they are immune to these problems, but are not currently used.
The reason for the lack of interest in shock-fitting methods can certainly be traced to the difficulty in developing general purpose codes based upon the shock-fitting technique. Indeed, in the past the shift from a shock-capturing to a shock-fitting discretization required a great effort and the resulting shock-fitting code had often strong limitations in the application.
As said above, a very critical element of the shock-fitting techniques is represented by the fact that the shock-fitting code must be able to make the topology of the computational grid compatible with the shock position.
The shock-fitting technique, that the PI introduced in Ref. [10] and developed in Refs. [11-13], simplified this algorithmic task in the context of solvers for unstructured grids. However, the most significant contribution to the simplification of this task came from Ref [15]. This new technique has made it possible to completely remove the aforementioned problem and, therefore, has opened the door to the development of new shock-fitting techniques for structured solvers which is the objective of this research.
The extension of this new shock-fitting technique to structured solvers and, in particular, to high accuracy ones could make an important contribution to the numerical simulation of turbulence and aeroacoustics. Indeed, the shock-capturing solvers for structured grids are used for their better performances than the unstructured ones in the simulation of turbulent flows with shocks through DNS and LES approach and in the acoustic direct simulation. However, the numerical problems related to the shock capture process (the reduction of the order of accuracy downstream of the shock, the generation of spurious waves, the numerical thickness of the shock wave) reduces the quality of the results, and introduces artifacts [ 2-5,23,24]
For these reasons, the development of a new class of high accuracy solvers for structured grids based on shock-fitting able to be used in DNS and LES and direct acoustic simulations certainly represents a step forward in computational fluid dynamics.
References:
see section "Eventuali altri partner esterni e ruolo nel progetto"