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Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection‐dominated flows

dc.contributor.authorFidkowski, Krzysztof J.en_US
dc.date.accessioned2011-12-05T18:34:10Z
dc.date.available2013-02-01T20:26:18Zen_US
dc.date.issued2011-12-23en_US
dc.identifier.citationFidkowski, Krzysztof J. (2011). "Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection‐dominated flows." International Journal for Numerical Methods in Engineering 88(12): 1297-1322. <http://hdl.handle.net/2027.42/88080>en_US
dc.identifier.issn0029-5981en_US
dc.identifier.issn1097-0207en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/88080
dc.description.abstractWe study practical strategies for estimating numerical errors in scalar outputs calculated from unsteady simulations of convection‐dominated flows, including those governed by the compressible Navier–Stokes equations. The discretization is a discontinuous Galerkin finite element method in space and time on static spatial meshes. Time‐integral quantities are considered for scalar outputs and these are shown to superconverge with temporal refinement. Output error estimates are calculated using the adjoint‐weighted residual method, where the unsteady adjoint solution is obtained using a discrete approach with an iterative solver. We investigate the accuracy versus computational cost trade‐off for various approximations of the fine‐space adjoint and find that exact adjoint solutions are accurate but expensive. To reduce the cost, we propose a local temporal reconstruction that takes advantage of superconvergence properties at Radau points, and a spatial reconstruction based on nearest‐neighbor elements. This inexact adjoint yields output error estimates at a computational cost of less than 2.5 times that of the forward problem for the cases tested. The calculated error estimates account for numerical error arising from both the spatial and temporal discretizations, and we present a method for identifying the percentage contributions of each discretization to the output error. Copyright © 2011 John Wiley & Sons, Ltd.en_US
dc.publisherJohn Wiley & Sons, Ltd.en_US
dc.subject.otherVerificationen_US
dc.subject.otherDiscontinuous Galerkinen_US
dc.subject.otherNavier–Stokesen_US
dc.subject.otherUnsteady Adjointen_US
dc.subject.otherOutput Erroren_US
dc.titleOutput error estimation strategies for discontinuous Galerkin discretizations of unsteady convection‐dominated flowsen_US
dc.typeArticleen_US
dc.rights.robotsIndexNoFollowen_US
dc.subject.hlbsecondlevelEngineering (General)en_US
dc.subject.hlbsecondlevelMechanical Engineeringen_US
dc.subject.hlbtoplevelEngineeringen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Aerospace Engineering, University of Michigan, 1320 Beal Avenue 3029 FXB, Ann Arbor, MI 48109, U.S.A.en_US
dc.contributor.affiliationumDepartment of Aerospace Engineering, University of Michigan, 1320 Beal Avenue 3029 FXB, Ann Arbor, MI 48109, U.S.A.en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/88080/1/3224_ftp.pdf
dc.identifier.doi10.1002/nme.3224en_US
dc.identifier.sourceInternational Journal for Numerical Methods in Engineeringen_US
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dc.owningcollnameInterdisciplinary and Peer-Reviewed


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