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POD-(H)DG Method for Incompressible Flow Simulations

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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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Authors and Affiliations

  1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA

    Guosheng Fu

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Zhu Wang

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  1. Guosheng Fu
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  2. Zhu Wang
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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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  • DOI: https://doi.org/10.1007/s10915-020-01328-4

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