Detecting troubled-cells on two-dimensional unstructured grids using a neural network

In a recent paper [Ray and Hesthaven, J. Comput. Phys. 367 (2018), pp 166-191], 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 articial 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.

Nov 01 2018

 Record created 2018-11-01, last modified 2019-06-19

Download fulltext

Rate this document:

Rate this document:
(Not yet reviewed)