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

被引:38
|
作者
Discacciati, Niccolo [1 ]
Hesthaven, Jan S. [1 ]
Ray, Deep [2 ]
机构
[1] Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland
[2] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA
关键词
Conservation laws; Discontinuous Galerkin; Artificial viscosity; Artificial neural networks; CONSERVATION-LAWS; RIEMANN PROBLEM; IMPLEMENTATION;
D O I
10.1016/j.jcp.2020.109304
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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.
引用
收藏
页数:30
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