Study of Mach reflection in inviscid flows

TL;DR

This study employs a high-order discontinuous Galerkin method with overset grids to accurately simulate Mach reflection phenomena in inviscid flows, capturing discontinuities and analyzing transition criteria.

Contribution

Introduces a novel shock capturing procedure using overset grids and troubled cell indicators for precise Mach reflection simulation in inviscid flows.

Findings

Accurately determined detachment and Von Neumann criteria for Mach flows.

Computed Mach stem heights for various wedge angles and Mach numbers.

Demonstrated hysteresis in the transition from regular to Mach reflection.

Abstract

In this paper, we study the Mach reflection phenomenon in inviscid flows using a higher order discontinuous Galerkin method and overset grids. We use the shock capturing procedure proposed in Siva Prasad Kochi et al. using overset grids to capture the discontinuities occurring in the supersonic flow over a wedge accurately. In this procedure, we obtain a coarse grid solution first and using the troubled cell data, we construct an overset grid which is approximately aligned to all the discontinuities. We rerun the solver with the coarse grid solution as the initial condition while using the troubled cell indicator and the limiter only on the overset grid. This allows us to capture the discontinuities accurately. Using this procedure, we have obtained the solution for Mach $3.0$ and $4.0$ flow over a wedge for various wedge angles and determined the detachment criterion and the Von Neumann condition accurately. We have also determined the Mach stem height for various wedge angles for these Mach numbers. We have also demonstrated the hysteresis that occurs in the transition from regular reflection to Mach reflection.