An improved ducros sensor for the simulation of compressible flows with shocks

Originally designed to distinguish shocks in turbulent flows, the Ducros sensor becomes very sensitive to any flow divergence in regions of negligible vorticity, and may significantly alter the solution. We present an improvement to the Ducros sensor for use in high speed flows where shocks are present. The accurate simulation of transitional and turbulent flows with shocks requires that dissipation be added only where necessary to stabilize the solution. However, adding too much dissipation can cause small scale structures to be damped out of the solution. We propose a modification to the Ducros sensor that is less sensitive in regions of negligible vorticity, but adds an appropriate amount of dissipation in regions of discontinuity. We present two test cases to demonstrate the proposed switch’s improvement over the original Ducros sensor: a forward facing step and a double ramp.