POD-(H)DG Method for Incompressible Flow Simulations

Abstract

We present a reduced order method based on proper orthogonal decomposition for the viscous Burgers’ equation and the incompressible Navier–Stokes equations discretized using an implicit-explicit hybrid discontinuous Galerkin/discoutinuous Galerkin (IMEX HDG/DG) scheme. A novel closure model, which can be easily computed offline, is introduced. Numerical results are presented to test the proposed POD model and the closure model.

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Data Availibility Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request

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Correspondence to Guosheng Fu.

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Guosheng Fu gratefully acknowledges the partial support of this work from U.S. National Science Foundation through Grant DMS-2012031. Zhu Wang gratefully acknowledges the partial support of this work from U.S. National Science Foundation through Grant DMS-1913073 and Office of the Vice President for Research at the University of South Carolina through an ASPIRE grant.

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Fu, G., Wang, Z. POD-(H)DG Method for Incompressible Flow Simulations. J Sci Comput 85, 24 (2020). https://doi.org/10.1007/s10915-020-01328-4

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Keywords

  • HDG
  • DG
  • POD
  • Burgers’ equation
  • Navier–Stokes equations

Mathematics Subject Classification

  • 65N30
  • 65N12
  • 76S05
  • 76D07