A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes

Lipnikov, Konstantin; Morgan, Nathaniel

doi:10.1016/j.jcp.2019.108931

Title: A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes

Authors:

Lipnikov, Konstantin;

Publication Date:: Sun Dec 01 00:00:00 EST 2019

Sponsoring Org.:: USDOE

OSTI Identifier:: 1567712

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Name: Journal of Computational Physics Journal Volume: 399 Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Citation Formats


                    Lipnikov, Konstantin, and Morgan, Nathaniel. A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes.  United States: N. p., 2019. 
Web.  doi:10.1016/j.jcp.2019.108931.

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                    Lipnikov, Konstantin, & Morgan, Nathaniel. A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes.  United States.  https://doi.org/10.1016/j.jcp.2019.108931

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                    Lipnikov, Konstantin, and Morgan, Nathaniel. Sun .  
"A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes".  United States.  https://doi.org/10.1016/j.jcp.2019.108931.

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@article{osti_1567712,

  title        = {A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes},

  author       = {Lipnikov, Konstantin and Morgan, Nathaniel},

  abstractNote = {},

  doi          = {10.1016/j.jcp.2019.108931},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 399,

  place        = {United States},

  year         = {Sun Dec 01 00:00:00 EST 2019},

  month        = {Sun Dec 01 00:00:00 EST 2019}

}

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https://doi.org/10.1016/j.jcp.2019.108931

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Works referenced in this record:

A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems
journal, February 2004

Loubère, R.; Ovadia, J.; Abgrall, R.
International Journal for Numerical Methods in Fluids, Vol. 44, Issue 6
DOI: 10.1002/fld.665

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets
journal, November 2017

Jibben, Z.; Herrmann, M.
Journal of Computational Physics, Vol. 349
DOI: 10.1016/j.jcp.2017.08.035

Quantum Hydrodynamic Simulation of Hysteresis in the Resonant Tunneling Diode
journal, March 1995

Chen, Zhangxin; Cockburn, Bernardo; Gardner, Carl L.
Journal of Computational Physics, Vol. 117, Issue 2
DOI: 10.1006/jcph.1995.1065

Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations
journal, May 1987

Dukowicz, John K.; Kodis, John W.
SIAM Journal on Scientific and Statistical Computing, Vol. 8, Issue 3
DOI: 10.1137/0908037

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation
journal, April 2017

Anderson, R.; Dobrev, V.; Kolev, Tz.
Journal of Computational Physics, Vol. 334
DOI: 10.1016/j.jcp.2016.12.031

Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations
journal, May 2000

Lepsky, Olga; Hu, Changqing; Shu, Chi-Wang
Applied Numerical Mathematics, Vol. 33, Issue 1-4
DOI: 10.1016/S0168-9274(99)00109-9

An efficient, accurate, simple ale method for nonlinear finite element programs
journal, March 1989

Benson, David J.
Computer Methods in Applied Mechanics and Engineering, Vol. 72, Issue 3
DOI: 10.1016/0045-7825(89)90003-0

The cell-centered discontinuous Galerkin method for Lagrangian compressible Euler equations in two-dimensions
journal, June 2014

Li, Zhenzhen; Yu, Xijun; Jia, Zupeng
Computers & Fluids, Vol. 96
DOI: 10.1016/j.compfluid.2014.03.018

An arbitrary Lagrangian-Eulerian computing method for all flow speeds
journal, March 1974

Hirt, C. W.; Amsden, A. A.; Cook, J. L.
Journal of Computational Physics, Vol. 14, Issue 3
DOI: 10.1016/0021-9991(74)90051-5

A high-order Lagrangian discontinuous Galerkin hydrodynamic method for quadratic cells using a subcell mesh stabilization scheme
journal, June 2019

Liu, Xiaodong; Morgan, Nathaniel R.; Burton, Donald E.
Journal of Computational Physics, Vol. 386
DOI: 10.1016/j.jcp.2019.02.008

Second-order sign-preserving conservative interpolation (remapping) on general grids
journal, January 2003

Margolin, L. G.; Shashkov, Mikhail
Journal of Computational Physics, Vol. 184, Issue 1
DOI: 10.1016/S0021-9991(02)00033-5

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics
journal, January 2012

Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
SIAM Journal on Scientific Computing, Vol. 34, Issue 5
DOI: 10.1137/120864672

Integration and homogeneous functions
journal, January 1999

Lasserre, Jean B.
Proceedings of the American Mathematical Society, Vol. 127, Issue 3
DOI: 10.1090/S0002-9939-99-04930-8

The local discontinuous Galerkin method for contaminant transport
journal, October 2000

Aizinger, Vadym; Dawson, Clint; Cockburn, Bernardo
Advances in Water Resources, Vol. 24, Issue 1
DOI: 10.1016/S0309-1708(00)00022-1

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method
journal, June 2010

Loubère, Raphaël; Maire, Pierre-Henri; Shashkov, Mikhail
Journal of Computational Physics, Vol. 229, Issue 12
DOI: 10.1016/j.jcp.2010.03.011

An efficient linearity-and-bound-preserving remapping method
journal, July 2003

Kucharik, Milan; Shashkov, Mikhail; Wendroff, Burton
Journal of Computational Physics, Vol. 188, Issue 2
DOI: 10.1016/S0021-9991(03)00187-6

Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics
journal, July 2012

Vilar, François
Computers & Fluids, Vol. 64
DOI: 10.1016/j.compfluid.2012.05.001

The nonconforming virtual element method
journal, May 2016

Ayuso de Dios, Blanca; Lipnikov, Konstantin; Manzini, Gianmarco
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50, Issue 3
DOI: 10.1051/m2an/2015090

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
journal, November 2010

Zhang, Xiangxiong; Shu, Chi-Wang
Journal of Computational Physics, Vol. 229, Issue 23
DOI: 10.1016/j.jcp.2010.08.016

High-Resolution Conservative Algorithms for Advection in Incompressible Flow
journal, April 1996

LeVeque, Randall J.
SIAM Journal on Numerical Analysis, Vol. 33, Issue 2
DOI: 10.1137/0733033

Fully multidimensional flux-corrected transport algorithms for fluids
journal, June 1979

Zalesak, Steven T.
Journal of Computational Physics, Vol. 31, Issue 3
DOI: 10.1016/0021-9991(79)90051-2

The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy
journal, October 1998

Caramana, E. J.; Burton, D. E.; Shashkov, M. J.
Journal of Computational Physics, Vol. 146, Issue 1
DOI: 10.1006/jcph.1998.6029

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations
journal, February 2011

Nguyen, N. C.; Peraire, J.; Cockburn, B.
Journal of Computational Physics, Vol. 230, Issue 4
DOI: 10.1016/j.jcp.2010.10.032

Incremental Remapping as a Transport/Advection Algorithm
journal, May 2000

Dukowicz, John K.; Baumgardner, John R.
Journal of Computational Physics, Vol. 160, Issue 1
DOI: 10.1006/jcph.2000.6465

On the Computation of Steady Hopper Flows
journal, January 2001

Gremaud, Pierre A.; Matthews, John V.
Journal of Computational Physics, Vol. 166, Issue 1
DOI: 10.1006/jcph.2000.6641

A Lagrangian discontinuous Galerkin hydrodynamic method
journal, February 2018

Liu, Xiaodong; Morgan, Nathaniel R.; Burton, Donald E.
Computers & Fluids, Vol. 163
DOI: 10.1016/j.compfluid.2017.12.007

A Local Discontinuous Galerkin Method for KdV Type Equations
journal, January 2002

Yan, Jue; Shu, Chi-Wang
SIAM Journal on Numerical Analysis, Vol. 40, Issue 2
DOI: 10.1137/S0036142901390378

Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
journal, October 2015

Chin, Eric B.; Lasserre, Jean B.; Sukumar, N.
Computational Mechanics, Vol. 56, Issue 6
DOI: 10.1007/s00466-015-1213-7

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

Basic Principles of Virtual Element Methods
journal, November 2012

BeirÃO Da Veiga, L.; Brezzi, F.; Cangiani, A.
Mathematical Models and Methods in Applied Sciences, Vol. 23, Issue 01
DOI: 10.1142/S0218202512500492

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

Bassi, F.; Rebay, S.
Journal of Computational Physics, Vol. 138, Issue 2
DOI: 10.1006/jcph.1997.5454

A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
journal, November 2014

Vilar, François; Maire, Pierre-Henri; Abgrall, Rémi
Journal of Computational Physics, Vol. 276
DOI: 10.1016/j.jcp.2014.07.030

Application of low-order Discontinuous Galerkin methods to the analysis of viscoelastic flows
journal, April 1994

Baaijens, Frank P. T.
Journal of Non-Newtonian Fluid Mechanics, Vol. 52, Issue 1
DOI: 10.1016/0377-0257(94)85057-7

Monotonicity in high-order curvilinear finite element arbitrary Lagrangian-Eulerian remap: MONOTONICITY IN HIGH-ORDER CURVILINEAR FINITE ELEMENT ALE REMAP
journal, October 2014

Anderson, R. W.; Dobrev, V. A.; Kolev, Tz. V.
International Journal for Numerical Methods in Fluids, Vol. 77, Issue 5
DOI: 10.1002/fld.3965

3D unstructured mesh ALE hydrodynamics with the upwind discontinuous finite element method
journal, May 1998

Kershaw, David S.; Prasad, Manoj K.; Shaw, Michael J.
Computer Methods in Applied Mechanics and Engineering, Vol. 158, Issue 1-2
DOI: 10.1016/S0045-7825(97)00228-4

Multi-Material ALE methods in unstructured grids
journal, July 2000

Peery, James S.; Carroll, Daniel E.
Computer Methods in Applied Mechanics and Engineering, Vol. 187, Issue 3-4
DOI: 10.1016/S0045-7825(99)00341-2

3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement
journal, May 2017

Morgan, Nathaniel R.; Waltz, Jacob I.
Journal of Computational Physics, Vol. 336
DOI: 10.1016/j.jcp.2017.02.030

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Title: A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes

Citation Formats

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Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations journal, May 1987

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation journal, April 2017

Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations journal, May 2000

An efficient, accurate, simple ale method for nonlinear finite element programs journal, March 1989

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An arbitrary Lagrangian-Eulerian computing method for all flow speeds journal, March 1974

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Second-order sign-preserving conservative interpolation (remapping) on general grids journal, January 2003

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The local discontinuous Galerkin method for contaminant transport journal, October 2000

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method journal, June 2010

An efficient linearity-and-bound-preserving remapping method journal, July 2003

Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics journal, July 2012

The nonconforming virtual element method journal, May 2016

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High-Resolution Conservative Algorithms for Advection in Incompressible Flow journal, April 1996

Fully multidimensional flux-corrected transport algorithms for fluids journal, June 1979

The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy journal, October 1998

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations journal, February 2011

Incremental Remapping as a Transport/Advection Algorithm journal, May 2000

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A Lagrangian discontinuous Galerkin hydrodynamic method journal, February 2018

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Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra journal, October 2015

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

Basic Principles of Virtual Element Methods journal, November 2012

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

A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids journal, November 2014

Application of low-order Discontinuous Galerkin methods to the analysis of viscoelastic flows journal, April 1994

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3D unstructured mesh ALE hydrodynamics with the upwind discontinuous finite element method journal, May 1998

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3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement journal, May 2017

A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems
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An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets
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Quantum Hydrodynamic Simulation of Hysteresis in the Resonant Tunneling Diode
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Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations
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High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation
journal, April 2017

Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations
journal, May 2000

An efficient, accurate, simple ale method for nonlinear finite element programs
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The cell-centered discontinuous Galerkin method for Lagrangian compressible Euler equations in two-dimensions
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An arbitrary Lagrangian-Eulerian computing method for all flow speeds
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A high-order Lagrangian discontinuous Galerkin hydrodynamic method for quadratic cells using a subcell mesh stabilization scheme
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Second-order sign-preserving conservative interpolation (remapping) on general grids
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Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics
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The nonconforming virtual element method
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On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
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The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy
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An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations
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Incremental Remapping as a Transport/Advection Algorithm
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On the Computation of Steady Hopper Flows
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A Lagrangian discontinuous Galerkin hydrodynamic method
journal, February 2018

A Local Discontinuous Galerkin Method for KdV Type Equations
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Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
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The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
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A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
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