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首页> 外文期刊>Journal of Computational Physics >Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks
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Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

机译：使用神经网络调整的人工粘度控制高阶不连续的Galerkin方案中的控制振荡

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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.
机译：用于保护法的高阶数值求解器遭受吉布斯现象，接近不连续性，导致杂散振荡和对溶液精度的不利影响。减少它的可能策略包括添加适当量的人工耗散。尽管在文献中提出了几种粘度模型，但它们对依赖性参数的依赖通常会限制它们的性能。其目的是构建普遍的人工粘度方法，我们提出了一种基于神经网络的新技术，集成到跑步 - 库塔塔不连续的Galerkin解算器中。提出了数值结果来证明基于网络的技术的性能。我们表明它能够保证最佳的准确性，以实现平稳问题，并准确地检测不连续性，必须注入耗散。执行与某些经典模型的比较，表明基于网络的模型始终处于传统优化模型中最好的，独立于所选择的问题和参数。 （c）2020 Elsevier Inc.保留所有权利。

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