Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amount of artificial dissipation. Although several viscosity models have been proposed in the literature, their dependence on problem-dependent parameters often limits their performances. Motivated by the objective to construct a universal artificial viscosity method, we propose a new technique based on neural networks, integrated into a Runge-Kutta Discontinuous Galerkin solver. Numerical results are presented to demonstrate the performance of this network-based technique. We show that it is able both to guarantee optimal accuracy for smooth problems, and to accurately detect discontinuities, where dissipation has to be injected. A comparison with some classical models is carried out, showing that the network-based model is always at par with the best among the traditional optimized models, independently of the selected problem and parameters. (C) 2020 Elsevier Inc. All rights reserved.


Published in:
Journal Of Computational Physics, 409, 109304
Year:
May 15 2020
Publisher:
San Diego, ACADEMIC PRESS INC ELSEVIER SCIENCE
ISSN:
0021-9991
1090-2716
Keywords:
Laboratories:




 Record created 2020-04-16, last modified 2020-10-27


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