TY - JOUR
T1 - Non-intrusive reduced order modeling of convection dominated flows using artificial neural networks with application to Rayleigh-Taylor instability
AU - Gao, Zhen
AU - Liu, Qi
AU - Hesthaven, Jan S.
AU - Wang, Bao Shan
AU - Don, Wai Sun
AU - Wen, Xiao
N1 - Publisher Copyright:
© 2021 Global Science Press. All rights reserved.
The authors would like to acknowledge the funding support of this research by the National Natural Science Foundation of China (11871443) and Shandong Provincial Qingchuang Science and Technology Project (2019KJI002). The author (Don) also likes to thank the Ocean University of China for providing the startup funding (201712011) that is used in supporting this work.
PY - 2021/7
Y1 - 2021/7
N2 - 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 singlemode 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. c 2021 Global-Science Press.
AB - 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 singlemode 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. c 2021 Global-Science Press.
KW - Adaptive sampling method
KW - Artificial neural network
KW - Non-intrusive reduced basis method
KW - Proper orthogonal decomposition
KW - Rayleigh-Taylor instability
UR - http://www.scopus.com/inward/record.url?scp=85106371478&partnerID=8YFLogxK
UR - https://global-sci.com/article/90824/non-intrusive-reduced-order-modeling-of-convection-dominated-flows-using-artificial-neural-networks-with-application-to-rayleigh-taylor-instability
U2 - 10.4208/CICP.OA-2020-0064
DO - 10.4208/CICP.OA-2020-0064
M3 - Journal article
AN - SCOPUS:85106371478
SN - 1815-2406
VL - 30
SP - 97
EP - 123
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 1
ER -
