Conservative shock filtering of numerical solutions of the 1-D Euler equations

We consider a recently developed conservative shock filter model in order to postprocess numerical solutions of the 1-D Euler equations of gas dynamics. The shock filtering process involves the definition of an indicator selecting the data regime where the filter is applied. Illustrated by several classical numerical test problems, we show that the use of simple indicators based on physical principles results in very accurate approximations of shocks and contact discontinuities.