Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

JOURNAL OF COMPUTATIONAL PHYSICS

卷:431

Article

Schwander, Lukas¹  Ray, Deep²  Hesthaven, Jan S.³ 

[1] Swiss Fed Inst Technol, CH-8092 Zurich, Switzerland

[2] Univ Southern Calif, Dept Aerosp & Mech Engn, Los Angeles, CA 90007 USA

[3] Ecole Polytech Fed Lausanne, Inst Math, Computat Math & Simulat Sci MCSS, CH-1015 Lausanne, Switzerland

关键词: Conservation laws;    Spectral methods;    Artificial viscosity;    Neural networks;    Gibbs oscillations;   

DOI  :  10.1016/j.jcp.2021.110144

来源: Elsevier

【 摘 要 】

While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution regularity is generally required. In this work we demonstrate how to train and use a local artificial neural network to estimate the local solution regularity and demonstrate the efficiency of nonlinear artificial viscosity methods based on this, in the context of Fourier spectral methods. We compare with entropy viscosity techniques and illustrate the promise of the neural network based estimators when solving one- and two-dimensional conservation laws, including the Euler equations. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free