  In this paper, eight different troubled cell indicators (shock detectors) are
reviewed for the solution of nonlinear hyperbolic conservation laws using
discontinuous Galerkin (DG) method and a WENO limiter on both structured and
unstructured meshes. Extensive simulations using one-dimensional and
two-dimensional problems (2D Riemann problem and the double Mach reflection)
for various orders on the hyperbolic system of Euler equations are used to
compare these troubled cell indicators. They are evaluated based on the
percentage of cells flagged as troubled cells for various orders and various
grid sizes. CPU time taken to test a single cell for discontinuity is also
compared. For one-dimensional problems, the performance of Fu and Shu indicator
and the modified KXRCF indicator is better than other indicators. For
two-dimensional problems, the performance of the artificial neural network
(ANN) indicator of Ray and Hesthaven is quite good and the Fu and Shu and the
modified KXRCF indicators are also good. These three indicators are suitable
candidates for applications of DGM using WENO limiters though it should be
noted that the ANN indicator is quite expensive and requires a lot of training.
