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

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...

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Bibliographic Details
Published in:	Computer methods in applied mechanics and engineering 2019-09, Vol.354, p.307-330
Main Authors:	Xiao, D., Fang, F., Heaney, C.E., Navon, I.M., Pain, C.C.
Format:	Article
Language:	eng
Subjects:	Aerodynamics Air flow Boundary conditions Computational fluid dynamics Coupling Cylinders Decomposition Domain decomposition Domain decomposition methods Fluid flow Hyperspaces Incompressibility Non-intrusive Proper Orthogonal Decomposition Radial basis function Reduced order modelling Reduced order models Street canyons Three dimensional flow Two dimensional flow
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Summary:	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. •A domain decomposition non-intrusive reduced order model (DDNIROM) is presented.•The DDNIROM exhibits good agreement with the high fidelity model (HFM).•Local hypersurfaces of the DDNIROM are based on radial basis functions.•These hypersurfaces represent the coupling between the subdomains.•The DDNIROM can be constructed without modification to the source code of the HFM.
ISSN:	0045-7825 1879-2138