Parameterized nonintrusive reduced‐order model for general unsteady flow problems using artificial neural networks

The last decades have been driven by significant progress in the computational capacity, which have been supporting the development of increasingly realistic and detailed simulations. However, despite these improvements, several problems still do not have an effective solution, due to their numerical complexity. As a result, the answer to these problems can be improved by using techniques that enable the description of phenomena with less resolution, but with lower computational costs, which is the case of the reduced order models. The main objective of this article is the presentation of a new approach for reduced order model development and application in the design and optimization of structural parts. The selected method is the artificial neural networks. Artificial neural networks allow the prediction of certain variables based on a given dataset. Two typical case studies are addressed: the first is a fixed plate subjected to uniformly distributed pressure and the second is a reinforced panel also subjected to internal pressure, with regular reinforcements to improve the specific strength. With this method, a substantial reduction in the simulation time is observed, being, approximately, 40 times faster than the solution obtained with Ansys. The developed neural network has a relative average difference of about 20 %, which is considered satisfactory given the complexity of the problem and considering it is a first application of these networks in this domain. In conclusion, this research made it possible to highlight the potential of reduced order model: including the shorter response time, the less computational resources, and the simplification of problems in detriment of less resolution in the description of structural behaviour. Given these advantages, it is expected that these models will play a key role in future applications, as in digital twins.

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Reduced Order Model for Unsteady Fluid Flows via Recurrent Neural Networks

Volume 2: CFD and FSI ◽

10.1115/omae2019-96543 ◽

2019 ◽

Author(s):

Sandeep B. Reddy ◽

Allan Ross Magee ◽

Rajeev K. Jaiman ◽

J. Liu ◽

W. Xu ◽

...

Keyword(s):

Neural Networks ◽

Reynolds Number ◽

Flow Field ◽

Unsteady Flow ◽

Recurrent Neural Networks ◽

Reduced Order Model ◽

Data Driven ◽

Order Model ◽

Reduced Order ◽

Low Dimensional

Abstract In this paper, we present a data-driven approach to construct a reduced-order model (ROM) for the unsteady flow field and fluid-structure interaction. This proposed approach relies on (i) a projection of the high-dimensional data from the Navier-Stokes equations to a low-dimensional subspace using the proper orthogonal decomposition (POD) and (ii) integration of the low-dimensional model with the recurrent neural networks. For the hybrid ROM formulation, we consider long short term memory networks with encoder-decoder architecture, which is a special variant of recurrent neural networks. The mathematical structure of recurrent neural networks embodies a non-linear state space form of the underlying dynamical behavior. This particular attribute of an RNN makes it suitable for non-linear unsteady flow problems. In the proposed hybrid RNN method, the spatial and temporal features of the unsteady flow system are captured separately. Time-invariant modes obtained by low-order projection embodies the spatial features of the flow field, while the temporal behavior of the corresponding modal coefficients is learned via recurrent neural networks. The effectiveness of the proposed method is first demonstrated on a canonical problem of flow past a cylinder at low Reynolds number. With regard to a practical marine/offshore engineering demonstration, we have applied and examined the reliability of the proposed data-driven framework for the predictions of vortex-induced vibrations of a flexible offshore riser at high Reynolds number.

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