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Title: A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

Abstract

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.

Authors:
 [1];  [2];  [2];  [3]
+ Show Author Affiliations
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
  2. North Carolina State Univ., Raleigh, NC (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1357240
Report Number(s):
INL/JOU-15-35604
Journal ID: ISSN 0271-2091
Grant/Contract Number:  
AC07-05ID14517
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Fluids
Additional Journal Information:
Journal Volume: 79; Journal Issue: 8; Journal ID: ISSN 0271-2091
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; implicit Runge-Kutta; discontinuous Galerkin; WENO; compressible Navier–Stokes; unsteady flows

Citation Formats

Xia, Yidong, Liu, Xiaodong, Luo, Hong, and Nourgaliev, Robert. A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations. United States: N. p., 2015. Web. doi:10.1002/fld.4057.
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Xia, Yidong, Liu, Xiaodong, Luo, Hong, & Nourgaliev, Robert. A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations. United States. https://doi.org/10.1002/fld.4057
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Xia, Yidong, Liu, Xiaodong, Luo, Hong, and Nourgaliev, Robert. Mon . "A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations". United States. https://doi.org/10.1002/fld.4057. https://www.osti.gov/servlets/purl/1357240.
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@article{osti_1357240,
title = {A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations},
author = {Xia, Yidong and Liu, Xiaodong and Luo, Hong and Nourgaliev, Robert},
abstractNote = {Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.},
doi = {10.1002/fld.4057},
journal = {International Journal for Numerical Methods in Fluids},
number = 8,
volume = 79,
place = {United States},
year = {Mon Jun 01 00:00:00 EDT 2015},
month = {Mon Jun 01 00:00:00 EDT 2015}
}
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https://doi.org/10.1002/fld.4057
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    Works referencing / citing this record:

    High-Order Hyperbolic Navier-Stokes Reconstructed Discontinuous Galerkin Method for Unsteady Flows
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