Numerical Detection of Shock Location and Shock Strength in Unsteady Flow Computations

Shock waves are regions of a high gradient in the numerical solution of high-speed flows. Numerical methods often have limited accuracy at shock waves. The use of shock sensors becomes vital to identify the shock regions in a flow field and make necessary changes in the numerical methods. Turbulence models used in Reynolds-averaged Navier-Stokes simulations also require modifications at shock waves, and these modifications often depend on the strength of the shock wave. Most of the shock sensors available in the literature predict the shock location, but they do not give any information about the shock properties. In this work, we propose a shock sensor obtained by solving a transport equation that predicts both the location and the strength of a shock in terms of the density ratio across the shock. The shock sensor is validated for a stationary shock and then used in unsteady flow simulation of single-diaphragm and double-diaphragm shock tubes. The sensitivity of the shock sensor to the parameters used in its transport equation, as well as its dependence on grid resolution is studied.