A numerical study on automatic mesh refinement for the simulation of Edney shock-shock interactions

The growing interest in hypersonic flight has motivated several research efforts devoted to the study of shock-shock interactions which can dramatically influence the heat load on different components of hypersonic aircraft. In the present work the use of an adaptive numerical scheme for the study of Edney type IV and type VI interactions is investigated. The numerical approach is based on a discontinuous Galerkin finite element method in which an h-adaptive algorithm is used to automatically refine the mesh in the regions where the most interesting flow structures are present. Several adaptation criteria are investigated. Furthermore, it is shown that the gradients obtained by the internal element reconstruction are not suitable for the computation of indicators because they are strongly affected by the shock capturing stabilisation. An alternative approach, based on the use of gradients obtained from a least-squared reconstruction which involves the neighbouring elements, is proposed.