An Unstructured, Three-Dimensional, Shock-Fitting Solver for Hypersonic Flows

Abstract

A novel unstructured shock-fitting algorithm for three-dimensional flows is presented in this paper. The fitted shock front is described using a double-sided, triangulated surface. Two sets of flow states, corresponding to the upstream and downstream sides of the discontinuity, are assigned to the gridpoints located on either side of the triangulated shock surface. This 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, are part of the overall tetrahedral grid. The fitted shock surface acts as an interior boundary for a shock-capturing solver that is used to solve the discretized governing equations in the smooth regions of the flowfield. Despite the intrinsic complexity of the algorithm and the need to include the extra computational nodes that make up the triangulated shock-surface, the algorithm is shown to provide high quality results even with the coarse grain tetrahedralizations used in the example provided. Moreover, the re-meshing step is limited to the region close to the shock surface and the fitting algorithm is only weakly coupled with the flow solver used in the simulation. The newly described algorithm is herein tested against an available reference solution which involves the hypersonic (M1 = 10) flow past a blunt-body featuring a spherical nose.