Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 317, Issue -, Pages 868-889Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.12.033
Keywords
Parameterized; Non-intrusive ROM; PDE; RBF; POD; Smolyak sparse grid
Funding
- Janet Watson scholarship at Department of ESE, Imperial College
- UK's Natural Environment Research Council [NER/A/S/2003/00595, NE/C52101X/1, NE/C51829X/1]
- Engineering and Physical Sciences Research Council [GR/R60898, EP/I00405X/1, EP/J002011/1]
- Imperial College High Performance Computing Service
- NSF/CMG grant [ATM-0931198]
- NSFC [11502241]
- BP Exploration
- EPSRC grant: Managing Air for Green Inner Cities (MAGIC) [EP/N010221/1]
- EPSRC MEMPHIS multi-phase flow programme grant [EP/K003976/1]
- EPSRC [EP/R005761/1, EP/J002011/1, EP/I00405X/1, EP/P013198/1, EP/N010221/1, EP/K003976/1, EP/I003002/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/N010221/1, EP/K003976/1, EP/I00405X/1, EP/I003002/1, EP/J002011/1, EP/P013198/1, EP/R005761/1] Funding Source: researchfish
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A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (ohm(p) is an element of R-P). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Op can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 [ 41,42]) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space. The new P-NIROM technique has been applied to parameterized Navier-Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out. (C) 2016 Elsevier B.V. All rights reserved.
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