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. Extensive simulations using one-dimensional and two-dimensional problems for various orders on the hyperbolic system of Euler equations are used to compare these troubled cell indicators. 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.

翻译：本文综述了八种不同的问题单元指示器（激波探测器），用于采用间断伽辽金（DG）方法和WENO限制器求解非线性双曲守恒律。通过一维和二维问题的广泛数值模拟，针对欧拉方程双曲系统的不同阶数，对这些问题单元指示器进行了比较。在一维问题中，Fu-Shu指示器与改进的KXRCF指示器的性能优于其他指示器。在二维问题中，Ray和Hesthaven提出的人工神经网络（ANN）指示器表现良好，同时Fu-Shu指示器与改进的KXRCF指示器性能亦佳。这三种指示器适用于采用WENO限制器的间断伽辽金方法的应用，但需注意ANN指示器计算成本较高且需要大量训练。