Numerical simulation of hypersonic flows past three-dimensional blunt bodies through a unstructured shock-fitting solver

Owing to the maturity nowadays reached by computational geometry, shock-fitting, i.e. treating shock waves as true surfaces of discontinuity may no longer be prohibitively complex, as commonly believed by CFD practitioners. In this paper we report on some newly implemented features and algorithmic improvements of an unstructured, shock-fitting algorithm for threedimensional flows that has been recently proposed by the authors. The shock wave is described using a double-sided triangulated surface which is allowed to float over a background tetrahedral grid while obeying to the Rankine-Hugoniot jump relations. A constrained, Delaunay tetrahedralization is applied in the neighbourhood of the shock-front to make sure that the triangular faces that make up the shock surface are part of the tetrahedral mesh that covers the entire computational domain. A shockcapturing, vertex-centred solver is used to discretise the governing PDEs in the smooth regions of the flow-field; it also allow to "capture" those shock waves that may not have been fitted and/or the interaction between different fitted shock surfaces. The capabilities of the technique are demonstrated by reference to the high speed flow past a blunt-nosed cylinder with a conical flare for which experimental and other numerical results are available. When the technique is compared with shock-capturing on un-adapted meshes of comparable resolution, it is shown that fitting the strong shocks allows to considerably improve the solution quality in the entire shock layer and over the body surface