An unstructured, three-dimensional, shock-fitting solver for hypersonic flows

A novel unstructured shock-fitting algorithm for three-dimensional flows is proposed in this paper. This new technique is able to work coupled with any unstructured vertex centred solver. The fitted shock front is described using a triangulated surface that is allowed to move, while obeying to the Rankine–Hugoniot jump relations, throughout a background tetrahedral mesh which covers the entire computational domain. At each time step, a local, constrained Delaunay tetrahedralization is applied in the neighbourhood of the shock front to ensure that the triangles, which make up the shock surface, belong to the overall tetrahedral grid. The fitted shock front acts as an interior boundary for the unstructured shock-capturing solver, used to solve the discretised governing equations in the smooth regions of the flow-field. The present algorithm has been tested against high speed flows past three-dimensional bodies, providing high quality results even using coarse grain tetrahedralization.

► Shock-capturing schemes are not flawless when used to simulate strong shocks.
► Most of these shortcomings can be relieved by fitting the shock wave.
► We propose a Shock-fitting scheme that operates on unstructured tetrahedral meshes.
► On similar grids, shock-fitting outperforms shock-capturing in terms of solution quality.