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Title: A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

Abstract

A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.

Authors:
 [1];  [1];  [1];  [2]
+ Show Author Affiliations
  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Mechanical and Aerospace Engineering
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Idaho National Laboratory (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1177217
Report Number(s):
INL/JOU-14-31336
Journal ID: ISSN 0045-7930
Grant/Contract Number:  
AC07-05ID14517
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 98; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Automatic differentiation; Discontinuous Galerkin; Hierarchical WENO reconstruction; Implicit Methods; Parallel computing

Citation Formats

Xia, Yidong, Luo, Hong, Frisbey, Megan, and Nourgaliev, Robert. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. United States: N. p., 2014. Web. doi:10.1016/j.compfluid.2014.01.023.
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Xia, Yidong, Luo, Hong, Frisbey, Megan, & Nourgaliev, Robert. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. United States. https://doi.org/10.1016/j.compfluid.2014.01.023
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Xia, Yidong, Luo, Hong, Frisbey, Megan, and Nourgaliev, Robert. Tue . "A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids". United States. https://doi.org/10.1016/j.compfluid.2014.01.023. https://www.osti.gov/servlets/purl/1177217.
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@article{osti_1177217,
title = {A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids},
author = {Xia, Yidong and Luo, Hong and Frisbey, Megan and Nourgaliev, Robert},
abstractNote = {A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.},
doi = {10.1016/j.compfluid.2014.01.023},
journal = {Computers and Fluids},
number = C,
volume = 98,
place = {United States},
year = {Tue Jul 01 00:00:00 EDT 2014},
month = {Tue Jul 01 00:00:00 EDT 2014}
}
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https://doi.org/10.1016/j.compfluid.2014.01.023
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Works referenced in this record:

The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
journal, April 1998

  • Cockburn, Bernardo; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 141, Issue 2
  • DOI: 10.1006/jcph.1998.5892

High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations
journal, December 1997

A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations
journal, March 1997

Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k–ω turbulence model equations
journal, May 2005

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
journal, December 1998

The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
journal, January 2008

  • Peraire, J.; Persson, P. -O.
  • SIAM Journal on Scientific Computing, Vol. 30, Issue 4
  • DOI: 10.1137/070685518

A High Order Discontinuous Galerkin Method for Compressible Turbulent Flows
book, January 2000

Space–time discontinuous Galerkin method for the compressible Navier–Stokes equations
journal, September 2006

  • Klaij, C. M.; van der Vegt, J. J. W.; van der Ven, H.
  • Journal of Computational Physics, Vol. 217, Issue 2
  • DOI: 10.1016/j.jcp.2006.01.018

Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
journal, January 2005

Hermite WENO schemes and their application as limiters for Runge–Kutta discontinuous Galerkin method: one-dimensional case
journal, January 2004

A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids
journal, October 2008

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • Journal of Computational Physics, Vol. 227, Issue 20
  • DOI: 10.1016/j.jcp.2008.06.035

High-order accurate implementation of solid wall boundary conditions in curved geometries
journal, January 2006

Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
journal, July 2004

An Interior Penalty Finite Element Method with Discontinuous Elements
journal, August 1982

  • Arnold, Douglas N.
  • SIAM Journal on Numerical Analysis, Vol. 19, Issue 4
  • DOI: 10.1137/0719052

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
journal, January 2002

  • Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo
  • SIAM Journal on Numerical Analysis, Vol. 39, Issue 5
  • DOI: 10.1137/S0036142901384162

Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier–Stokes equations
journal, January 2006

  • Hartmann, R.
  • International Journal for Numerical Methods in Fluids, Vol. 51, Issue 9-10
  • DOI: 10.1002/fld.1134

Pseudo-time stepping methods for space–time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations
journal, December 2006

  • Klaij, C. M.; van der Vegt, J. J. W.; van der Ven, H.
  • Journal of Computational Physics, Vol. 219, Issue 2
  • DOI: 10.1016/j.jcp.2006.04.003

A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids
journal, March 2013

A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
journal, September 2008

  • Dumbser, Michael; Balsara, Dinshaw S.; Toro, Eleuterio F.
  • Journal of Computational Physics, Vol. 227, Issue 18
  • DOI: 10.1016/j.jcp.2008.05.025

Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
journal, October 2009

A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes
journal, September 2007

  • Balsara, Dinshaw S.; Altmann, Christoph; Munz, Claus-Dieter
  • Journal of Computational Physics, Vol. 226, Issue 1
  • DOI: 10.1016/j.jcp.2007.04.032

A reconstructed discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids
journal, September 2010

  • Luo, Hong; Luo, Luqing; Nourgaliev, Robert
  • Journal of Computational Physics, Vol. 229, Issue 19
  • DOI: 10.1016/j.jcp.2010.05.033

A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids
journal, February 2011

A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids
journal, June 2012

A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems
journal, February 2012

A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
journal, February 2012

An Efficient Implicit Discontinuous Spectral Galerkin Method
journal, September 2001

  • Rasetarinera, Patrick; Hussaini, M. Y.
  • Journal of Computational Physics, Vol. 172, Issue 2
  • DOI: 10.1006/jcph.2001.6853

p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations
journal, July 2005

  • Fidkowski, Krzysztof J.; Oliver, Todd A.; Lu, James
  • Journal of Computational Physics, Vol. 207, Issue 1
  • DOI: 10.1016/j.jcp.2005.01.005

Implicit Discontinuous Galerkin Method for RANS Simulation Utilizing Pointwise Relaxation Algorithm
journal, June 2010

An implicit matrix-free Discontinuous Galerkin solver for viscous and turbulent aerodynamic simulations
journal, November 2011

An Implicit Method for a Reconstructed Discontinuous Galerkin Method on Tetrahedron Grids
conference, September 2012

  • Xia, Yidong; Luo, Hong; Nourgaliev, Robert
  • 42nd AIAA Fluid Dynamics Conference and Exhibit
  • DOI: 10.2514/6.2012-2834

Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows
journal, October 1997

  • Batten, P.; Leschziner, M. A.; Goldberg, U. C.
  • Journal of Computational Physics, Vol. 137, Issue 1
  • DOI: 10.1006/jcph.1997.5793

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids
journal, November 2012

  • Luo, Hong; Luo, Luqing; Nourgaliev, Robert
  • Communications in Computational Physics, Vol. 12, Issue 5
  • DOI: 10.4208/cicp.250911.030212a

A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
journal, January 2006

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • Journal of Computational Physics, Vol. 211, Issue 2
  • DOI: 10.1016/j.jcp.2005.06.019

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws
journal, July 2011

  • Xu, Zhiliang; Liu, Yingjie; Du, Huijing
  • Journal of Computational Physics, Vol. 230, Issue 17
  • DOI: 10.1016/j.jcp.2011.05.014

Fast p-Multigrid Discontinuous Galerkin Method for Compressible Flows at All Speeds
journal, March 2008

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • AIAA Journal, Vol. 46, Issue 3
  • DOI: 10.2514/1.28314

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986

  • Saad, Youcef; Schultz, Martin H.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
  • DOI: 10.1137/0907058

The Development of Discontinuous Galerkin Methods
book, January 2000

  • Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang
  • Lecture Notes in Computational Science and Engineering
  • DOI: 10.1007/978-3-642-59721-3_1

On the computation of steady-state compressible flows using a discontinuous Galerkin method
journal, January 2008

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • International Journal for Numerical Methods in Engineering, Vol. 73, Issue 5
  • DOI: 10.1002/nme.2081

A Fast, Matrix-free Implicit Method for Compressible Flows on Unstructured Grids
journal, November 1998

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • Journal of Computational Physics, Vol. 146, Issue 2
  • DOI: 10.1006/jcph.1998.6076

On the computation of compressible turbulent flows on unstructured grids
conference, August 2000

  • Luo, Hong; Sharov, Dmitri; Baum, Joseph
  • 38th Aerospace Sciences Meeting and Exhibit
  • DOI: 10.2514/6.2000-926

Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations
journal, August 2007

Three Dimensional Stabilized Finite Elements for Compressible Navier-Stokes
conference, June 2011

  • Erwin, Jon; Anderson, W. Kyle; Kapadia, Sagar
  • 20th AIAA Computational Fluid Dynamics Conference
  • DOI: 10.2514/6.2011-3411

Navier-Stokes computations of vortical flows over low-aspect-ratio wings
journal, February 1990

  • Thomas, James L.; Krist, Sherrie Taylor; Anderson, W. Kyle
  • AIAA Journal, Vol. 28, Issue 2
  • DOI: 10.2514/3.10376
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    Works referencing / citing this record:

    A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces
    journal, January 2020

    • Pandare, Aditya K.; Waltz, Jacob; Bakosi, Jozsef
    • International Journal for Numerical Methods in Fluids, Vol. 92, Issue 8
    • DOI: 10.1002/fld.4810

    Development of a nonconservative discontinuous Galerkin formulation for simulations of unsteady and turbulent flows
    journal, May 2020

    • Lv, Yu
    • International Journal for Numerical Methods in Fluids, Vol. 92, Issue 5
    • DOI: 10.1002/fld.4785

    High-Order Hyperbolic Navier-Stokes Reconstructed Discontinuous Galerkin Method for Unsteady Flows
    conference, June 2019

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