A Shock Sensor Based on Image Segmentation with Application to a Hybrid Central/WENO Scheme

Abstract

A novel shock sensor based on image segmentation is proposed for flows with shock or detonation waves. It consists of a function computed based on the numerical Schliren formulation, which is the absolute value of the density gradient. A fast segmentation technique is applied to the sensor function to determine the threshold of the sensor. The candidate troubled cells detected via the computed threshold are further filtered by a Ducros sensor and multiresolution analysis to exclude turbulent zones from the troubled cells. The proposed sensor is applied to a finite difference hybrid scheme, tested for several cases, and compared with other sensors, namely the Ducros sensor, the multiresolution analysis, and WENO- and TENO-based sensors. The results show that the proposed sensor detects the shock and detonation waves more accurately than the other sensors with fewer cells and reduces the computational time of the hybrid scheme.