Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

Year:    2021

Author:    Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don, Xiao Wen

Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 97–123

Abstract

A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws. Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers' equation with a parameterized diffusion coefficient. The two-dimensional single-mode Rayleigh-Taylor instability (RTI), where the amplitude of the small perturbation and time are considered as free parameters, is also simulated. An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN. The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/ 10.4208/cicp.OA-2020-0064

Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 97–123

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Rayleigh-Taylor instability non-intrusive reduced basis method proper orthogonal decomposition artificial neural network adaptive sampling method.

Author Details

Zhen Gao

Qi Liu

Jan S. Hesthaven

Bao-Shan Wang

Wai Sun Don

Xiao Wen