Abstract
In a recent paper (Ray and Hesthaven, 2018) [38], we proposed a new type of troubled-cell indicator to detect discontinuities in the numerical solutions of one-dimensional conservation laws. This was achieved by suitably training an artificial neural network on canonical local solution structures for conservation laws. The proposed indicator was independent of problem-dependent parameters, giving it an advantage over existing limiter-based indicators. In the present paper, we extend this approach to train a similar network capable of detecting troubled-cells on two-dimensional unstructured grids. The proposed network has a smaller architecture compared to its one-dimensional predecessor, making it computationally efficient. Several numerical results are presented to demonstrate the performance of the new indicator.
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