A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

File Description SizeFormat 
CMAME_697.pdfAccepted version1.42 MBAdobe PDFView/Open
Title: A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
Authors: Xiao, D
Fang, F
Pain, C
Navon, I
Item Type: Journal Article
Abstract: 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 e ffi cient approach for model reduction of parameterized partia l di ff eren- tial equations (P-PDEs). Over existing parameterized redu ced order models (P-ROM) (most of them are based on the reduced basis method), it is non -intrusive and inde- pendent on partial di ff erential equations and computational codes. During the tra ining process, the Smolyak sparse grid method is used to select a se t of parameters over a specific parameterized space ( Ω p ∈ R P ). For each selected parameter, the reduced ba- sis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function set s for any parameters over Ω p can be obtained using an interpolation method. The P-NIROM c an then be con- structed by using our recently developed technique [ 50 , 53 ] 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 redu ced space. The new P-NIROM technique has been applied to parameterized Navier-Stokes equations and implemented with an unstructured mesh finite e lement model. The ca- pability of this P-NIROM has been illustrated numerically b y two test cases: flow past a cylinder and lock exchange case. The prediction capabilit ies of the P-NIROM have been evaluated by varying the viscosity, initial and bounda ry conditions. The results show that this P-NIROM has captured the quasi-totality of th e details of the flow with CPU speedup of three orders of magnitude. An error analysis f or the P-NIROM has been carried out.
Issue Date: 16-Jan-2017
Date of Acceptance: 24-Dec-2016
URI: http://hdl.handle.net/10044/1/43587
DOI: https://dx.doi.org/10.1016/j.cma.2016.12.033
ISSN: 0045-7825
Publisher: Elsevier
Start Page: 868
End Page: 889
Journal / Book Title: Computer Methods in Applied Mechanics and Engineering
Volume: 317
Copyright Statement: © 2016 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/
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/K003976/1
RG80519
Keywords: Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Mathematics, Interdisciplinary Applications
Mechanics
Engineering
Mathematics
Parameterized
Non-intrusive ROM
PDE
RBF
POD
Smolyak sparse grid
PROPER ORTHOGONAL DECOMPOSITION
VARIATIONAL DATA ASSIMILATION
SHALLOW-WATER EQUATIONS
PETROV-GALERKIN METHODS
FINITE-ELEMENT METHODS
EMPIRICAL INTERPOLATION
SPARSE GRIDS
FLUID-FLOW
REDUCTION
STRATEGIES
Applied Mathematics
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering
Earth Science and Engineering



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx