Simple shock detector for discontinuous Galerkin method

Achieving highly accurate solutions is one of major motivations in simulating fluid flows. Among various methods in Computational Fluid Dynamics, the discontinuous Galerkin (DG) method has gained popularity due to the ability to obtain higher order solutions on arbitrary grids. However, the method is not widely adopted (yet) in industry due to several challenges in the implementation. One of those challenges is capturing a discontinuity. Many researchers developed strategies to capture this abrupt jump in a flow robustly in the DG method. Most of them are using information from neighboring cells to sense a discontinuity, which violates the local character of the DG algorithm and therefore increases the complexity. Furthermore, additional communication is inevitable which degrades the scaling performance, especially on massively parallel platforms. In this work, we propose a simple discontinuity sensor completely local to an element. By using self-information, one can minimize communication for sensing a discontinuity. Furthermore, by exploiting information from the proposed sensor, we suggest an automated procedure to determine a filtering strength to resolve a discontinuity.