TY - JOUR
T1 - A Data-Driven Scale-Invariant Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws
AU - Zhang , Zixuan
AU - Dong , Yidao
AU - Zou , Yuanyang
AU - Zhang , Hao
AU - Deng , Xiaogang
JO - Communications in Computational Physics
VL - 4
SP - 1120
EP - 1154
PY - 2024
DA - 2024/05
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0162
UR - https://global-sci.org/intro/article_detail/cicp/23096.html
KW - WCNS, neural network, machine learning, scale-invariant, shock-capturing.
AB - <p style="text-align: justify;">With continuous developments in various techniques, machine learning is
becoming increasingly viable and promising in the field of fluid mechanics. In this
article, we present a machine learning approach for enhancing the resolution and robustness of the weighted compact nonlinear scheme (WCNS). We employ a neural
network as a weighting function in the WCNS scheme and follow a data-driven approach to train this neural network. Neural networks can learn a new smoothness
measure and calculate a weight function inherently. To facilitate the machine learning task and train with fewer data, we integrate the prior knowledge into the learning
process, such as a Galilean invariant input layer and CNS polynomials. The normalization in the Delta layer (the so-called Delta layer is used to calculate input features)
ensures that the WCNS3-NN schemes achieve a scale-invariant property (Si-property)
with an arbitrary scale of a function, and an essentially non-oscillatory approximation of a discontinuous function (ENO-property). The Si-property and ENO-property
of the data-driven WCNS schemes are validated numerically. Several one- and two-dimensional benchmark examples, including strong shocks and shock-density wave
interactions, are presented to demonstrate the advantages of the proposed method.</p>