A data-driven shock capturing approach for discontinuous Galekin methods

We propose a data-driven artificial viscosity model for shock capturing in discontinuous Galerkin methods. The proposed model trains a multi-layer feedforward network to map from the element-wise solution to a smoothness indicator, based on which the amount of artificial viscosity is determined. The data set for the training of the network is obtained using canonical functions. The compactness of the data set, which is critical to the success of training the network, is ensured by normalization and the adjustment of the range of the smoothness indicator. The network is able to recover the expected smoothness much more reliably than its traditional counterpart, i.e. the averaged modal decay model. Several smooth and non-smooth test cases are considered to investigate the performance of this data-driven model. Convergence tests show that the proposed model recovers the accuracy of the corresponding inviscid schemes for smooth regions. For a wide range of non-smooth flows, the model is shown to suppress spurious oscillations well.