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

Yidong Xia; Xiaodong Liu; Hong Luo; Robert Nourgaliev

doi:10.1002/fld.4057

journal article Jun 18, 2015

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

Yidong Xia Xiaodong Liu

Hong Luo

Robert Nourgaliev

International Journal for Numerical Methods in Fluids Vol. 79 No. 8 pp. 416-435 · Wiley

View at Publisher Save 10.1002/fld.4057

Abstract

SummaryA 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. Copyright © 2015 John Wiley & Sons, Ltd.

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Details

Published: Jun 18, 2015
Vol/Issue: 79(8)
Pages: 416-435
License: View

Authors

Y

Yidong Xia

Idaho National Laboratory Idaho Falls Idaho USA

X

Xiaodong Liu

Department of Mechanical and Aerospace Engineering North Carolina State University Raleigh NC 27695 USA

H

Hong Luo

Department of Mechanical and Aerospace Engineering North Carolina State University Raleigh NC 27695 USA

R

Robert Nourgaliev

Design Physics Division Lawrence Livermore National Laboratory Livermore CA 94550 USA

Funding

Laboratory Directed Research and Development Award: 13-SI-002

U.S. Department of Energy Award: DE-AC52-07NA27344

Cite This Article

Yidong Xia, Xiaodong Liu, Hong Luo, et al. (2015). A third‐order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time‐accurate solution of the compressible Navier–Stokes equations. International Journal for Numerical Methods in Fluids, 79(8), 416-435. https://doi.org/10.1002/fld.4057

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

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