A domain decomposition method for the non-intrusive reduced order modelling of fluid flow

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Title: A domain decomposition method for the non-intrusive reduced order modelling of fluid flow
Authors: Xiao, D
Fang, F
Heaney, CE
Navon, IM
Pain, CC
Item Type: Journal Article
Abstract: In this paper we present a new domain decomposition non-intrusive reduced order model (DDNIROM) for the Navier–Stokes equations. The computational domain is partitioned into subdomains and a set of local basis functions is constructed in each subdomain using Proper Orthogonal Decomposition (POD). A radial basis function (RBF) method is then used to generate a set of hypersurfaces for each subdomain. Each local hypersurface represents, not only the fluid dynamics over the subdomain to which it belongs, but also the interactions with the surrounding subdomains. This implicit coupling between the subdomains provides the global coupling necessary to enforce incompressibility and is a means of providing boundary conditions for each subdomain. The performance of this DDNIROM is illustrated numerically by three examples: flow past a cylinder, and air flow over 2D and 3D street canyons. The results show that the DDNIROM exhibits good agreement with the high-fidelity full model while the computational cost is reduced by several orders of magnitude. The domain decomposition (DD) method provides the flexibility to choose different numbers of local basis functions for each subdomain depending on the complexity of the flow therein. The fact that the RBF surface representation takes input only from its current subdomain and the surrounding subdomains, means that, crucially, there is a reduction in the dimensionality of the hypersurface when compared with a more traditional, global NIROM. This comes at the cost of having a larger number of hypersurfaces.
Issue Date: 30-May-2019
Date of Acceptance: 23-May-2019
URI: http://hdl.handle.net/10044/1/70185
DOI: https://dx.doi.org/10.1016/j.cma.2019.05.039
ISSN: 0045-7825
Publisher: Elsevier BV
Journal / Book Title: Computer Methods in Applied Mechanics and Engineering
Copyright Statement: © 2019 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: 01 Mathematical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published online
Embargo Date: 2020-05-30
Online Publication Date: 2019-05-30
Appears in Collections:Earth Science and Engineering

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