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
JO - Communications in Computational Physics
VL - 1
SP - 97
EP - 123
PY - 2021
DA - 2021/04
SN - 30
DO - http://doi.org/ 10.4208/cicp.OA-2020-0064
UR - https://global-sci.org/intro/article_detail/cicp/18875.html
KW - Rayleigh-Taylor instability, non-intrusive reduced basis method, proper orthogonal
decomposition, artificial neural network, adaptive sampling method.
AB - <p style="text-align: justify;">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&#39; 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.</p>