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On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

Author
García Archilla, Bosco; Novo Martín, Juliauntranslated; Rubino, Samuele
Entity
UAM. Departamento de Matemáticas
Publisher
Elsevier
Date
2022-12-30
Citation
Computer Methods in Applied Mechanics and Engineering 405 (2023): 115866
ISSN
0045-7825 (print); 1879-2138 (online)
DOI
10.1016/j.cma.2022.115866
Funded by
Research is supported by Spanish MCINYU under grants PGC2018-096265-B-I00 and PID2019-104141GB-I00. Research is supported by Spanish MINECO under grants VA169P20. Research is supported by Spanish MCINYU under grant RTI2018-093521-B-C31 and by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Actions, grant agreement 872442-ARIA
Project
Gobierno de España. PGC2018-096265-B-I00; Gobierno de España. PID2019-104141GB-I00; Gobierno de España. RTI2018-093521-B-C31; info:eu-repo/grantAgreement/EC/H2020/872442
Editor's Version
https://doi.org/10.1016/j.cma.2022.115866
Subjects
Grad–div stabilization; Navier–Stokes equations; Nonlinear term discretization; Proper orthogonal decomposition; Matemáticas
URI
http://hdl.handle.net/10486/706560
Rights
© 2022 The Author(s)

Licencia de Creative Commons
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Abstract

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier–Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a full order method (FOM)) and a different discretization of the nonlinear term is applied in the POD method. We prove that an additional error term appears in this case, compared with the case in which the same discretization of the nonlinear term is applied for both the FOM and the POD methods. However, the added term has the same size as the error coming from the FOM so that the rate of convergence of the POD method is barely affected. We analyze the case in which we add grad–div stabilization to both the FOM and the POD methods because it allows to get error bounds with constants independent of inverse powers of the viscosity. We also study the case in which no stabilization is added. Some numerical experiments support the theoretical analysis
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Google™ Scholar:García Archilla, Bosco - Novo Martín, Julia - Rubino, Samuele

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