Shock capturing schemes with local mesh adaptation for high speed compressible flows on three dimensional unstructured grids

Abstract

This paper contributes towards a more complete approach to capture very strong shocks in various applications of high speed compressible Navier–Stokes flows including blasts and explosions using second order finite volume method on unstructured grids. The HLLC Riemann solver is employed to solve for fluxes at cell interfaces with second order approximation of local Riemann states, thus obtaining second order accuracy. In order to stabilize solutions due to high order approximation of solutions in the presence of discontinuities, several strategies are presented in this work. Slope limiters are first explored on unstructured grid to maintain monotonicity of the solution reconstruction following local extremum diminishing (LED) or total variation diminishing (TVD) criteria. The hybrid HLLC/HLLE scheme is appended to eliminate shock instabilities in very strong shock cases. To improve resolution of shocks, a local mesh adaptation scheme is used to increase mesh resolution in areas of high gradients. The scheme only regenerates mesh locally and is proven to be robust and efficient for capturing of unsteady shock propagation applications. Comparisons on the accuracy and performance of different methods on various applications are drawn to suggest a more robust and efficient method for capturing shocks on unstructured grids.