Extrapolated Shock Fitting for Two-Dimensional Flows on Structured Grids

Abstract

Over the years the development of structured-grid shock-fitting techniques faced two main problems: the handling of a moving discontinuity on a fixed background grid and the capability of simulating complex flow configurations. In the proposed work, the authors present a new shock-fitting technique for structured-grid solvers that is capable of overcoming the limitations that affected the different approaches originally developed. The technique presented here removes the tight link between grid topology and shock topology, which characterizes previous shock fitting as well as front tracking methods. This significantly simplifies their implementation and more importantly reduces the computational overhead related to these geometrical manipulations. Interacting discontinuities and shocks interacting with a solid boundary are discussed and analyzed. Finally, a quantitative investigation of the error reduction obtained with the approach proposed via a global grid convergence analysis is presented.