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Title: A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Abstract

Discontinuous Galerkin (DG) methods have been well established for single-material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. Here, a second-order DG(P1) method and a third-order least-squares based rDG(P1P2) are used to discretize this system in space, and a third-order total variation diminishing (TVD) Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second- and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-materialmore » system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high-order rDG method for multi-material hydrodynamics.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1739922
Alternate Identifier(s):
OSTI ID: 1595874
Report Number(s):
LA-UR-19-20312
Journal ID: ISSN 0271-2091
Grant/Contract Number:  
89233218CNA000001; 20170127ER
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Fluids
Additional Journal Information:
Journal Volume: 92; Journal Issue: 8; Journal ID: ISSN 0271-2091
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Non-equilibrium multi-material; Discontinuous Galerkin; Consistent discretizations

Citation Formats

Pandare, Aditya Kiran, Waltz, Jacob I., and Bakosi, Jozsef. A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces. United States: N. p., 2020. Web. doi:10.1002/fld.4810.
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Pandare, Aditya Kiran, Waltz, Jacob I., & Bakosi, Jozsef. A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces. United States. https://doi.org/10.1002/fld.4810
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Pandare, Aditya Kiran, Waltz, Jacob I., and Bakosi, Jozsef. Tue . "A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces". United States. https://doi.org/10.1002/fld.4810. https://www.osti.gov/servlets/purl/1739922.
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@article{osti_1739922,
title = {A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces},
author = {Pandare, Aditya Kiran and Waltz, Jacob I. and Bakosi, Jozsef},
abstractNote = {Discontinuous Galerkin (DG) methods have been well established for single-material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. Here, a second-order DG(P1) method and a third-order least-squares based rDG(P1P2) are used to discretize this system in space, and a third-order total variation diminishing (TVD) Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second- and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high-order rDG method for multi-material hydrodynamics.},
doi = {10.1002/fld.4810},
journal = {International Journal for Numerical Methods in Fluids},
number = 8,
volume = 92,
place = {United States},
year = {Tue Jan 14 00:00:00 EST 2020},
month = {Tue Jan 14 00:00:00 EST 2020}
}
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https://doi.org/10.1002/fld.4810
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Works referenced in this record:

The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
journal, April 1990

  • Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang
  • Mathematics of Computation, Vol. 54, Issue 190
  • DOI: 10.2307/2008501

Runge–Kutta discontinuous Galerkin method for the approximation of Baer and Nunziato type multiphase models
journal, June 2012

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces
journal, January 2015

  • Henry de Frahan, Marc T.; Varadan, Sreenivas; Johnsen, Eric
  • Journal of Computational Physics, Vol. 280
  • DOI: 10.1016/j.jcp.2014.09.030

An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach
journal, July 2014

Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection–diffusion equations on triangular meshes
journal, February 2013

Fully-implicit orthogonal reconstructed Discontinuous Galerkin method for fluid dynamics with phase change
journal, January 2016

Multicomponent Flow Calculations by a Consistent Primitive Algorithm
journal, May 1994

How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach
journal, April 1996

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

A simple algebraic interface capturing scheme using hyperbolic tangent function
journal, January 2005

  • Xiao, F.; Honma, Y.; Kono, T.
  • International Journal for Numerical Methods in Fluids, Vol. 48, Issue 9
  • DOI: 10.1002/fld.975

A sequel to AUSM, Part II: AUSM+-up for all speeds
journal, May 2006

Total variation diminishing Runge-Kutta schemes
journal, January 1998

  • Gottlieb, Sigal; Shu, Chi-Wang
  • Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221
  • DOI: 10.1090/S0025-5718-98-00913-2

A comparative study of multimaterial Lagrangian and Eulerian methods with pressure relaxation
journal, August 2013

On the computation of multi-material flows using ALE formulation
journal, February 2004

  • Luo, Hong; Baum, Joseph D.; Löhner, Rainald
  • Journal of Computational Physics, Vol. 194, Issue 1
  • DOI: 10.1016/j.jcp.2003.09.026

Multi-material closure model for high-order finite element Lagrangian hydrodynamics: CLOSURE MODEL FOR HIGH-ORDER FINITE ELEMENT HYDRODYNAMICS
journal, April 2016

  • Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.
  • International Journal for Numerical Methods in Fluids, Vol. 82, Issue 10
  • DOI: 10.1002/fld.4236

An enhanced AUSM $$^{+}$$ + -up scheme for high-speed compressible two-phase flows on hybrid grids
journal, September 2018

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

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

A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
journal, February 1996

  • Greenberg, J. M.; Leroux, A. Y.
  • SIAM Journal on Numerical Analysis, Vol. 33, Issue 1
  • DOI: 10.1137/0733001

A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows
journal, April 1999

  • Saurel, Richard; Abgrall, Rémi
  • Journal of Computational Physics, Vol. 150, Issue 2
  • DOI: 10.1006/jcph.1999.6187

A front-tracking method for viscous, incompressible, multi-fluid flows
journal, May 1992

Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
journal, January 2006

  • Parés, Carlos
  • SIAM Journal on Numerical Analysis, Vol. 44, Issue 1
  • DOI: 10.1137/050628052

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity
journal, December 2016

An implicit discontinuous Galerkin method for the unsteady compressible Navier–Stokes equations
journal, January 2012

A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme
journal, July 2007

Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations
journal, October 2001

  • Kapila, A. K.; Menikoff, R.; Bdzil, J. B.
  • Physics of Fluids, Vol. 13, Issue 10
  • DOI: 10.1063/1.1398042

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

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

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

A generalized approach for sub- and super-critical flows using the Local Discontinuous Galerkin method
journal, January 2013

  • Gryngarten, Leandro D.; Menon, Suresh
  • Computer Methods in Applied Mechanics and Engineering, Vol. 253
  • DOI: 10.1016/j.cma.2012.08.021

Closure models for multimaterial cells in arbitrary Lagrangian–Eulerian hydrocodes
journal, January 2008

  • Shashkov, M.
  • International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8
  • DOI: 10.1002/fld.1574

Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures
journal, March 2009

  • Richard Saurel, ; Petitpas, Fabien; Berry, Ray A.
  • Journal of Computational Physics, Vol. 228, Issue 5
  • DOI: 10.1016/j.jcp.2008.11.002

Multi-material pressure relaxation methods for Lagrangian hydrodynamics
journal, August 2013

Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)
journal, October 2015

Volume of fluid (VOF) method for the dynamics of free boundaries
journal, January 1981

Sharpening diffuse interfaces with compressible fluids on unstructured meshes
journal, July 2017

  • Chiapolino, Alexandre; Saurel, Richard; Nkonga, Boniface
  • Journal of Computational Physics, Vol. 340
  • DOI: 10.1016/j.jcp.2017.03.042

High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set
journal, June 2007

A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials
journal, November 1986

Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows
journal, October 2016

  • Barlow, Andrew J.; Maire, Pierre-Henri; Rider, William J.
  • Journal of Computational Physics, Vol. 322
  • DOI: 10.1016/j.jcp.2016.07.001

A comparative study of various pressure relaxation closure models for one-dimensional two-material Lagrangian hydrodynamics
journal, May 2010

  • Kamm, J. R.; Shashkov, M. J.; Fung, J.
  • International Journal for Numerical Methods in Fluids, Vol. 65, Issue 11-12
  • DOI: 10.1002/fld.2354

A numerical model for multiphase liquid–vapor–gas flows with interfaces and cavitation
journal, April 2019

A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows
journal, October 2018

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

An Arbitrary Lagrangian-Eulerian Reconstructed Discontinuous Galerkin method for Compressible Multiphase flows
conference, June 2016

  • Pandare, Aditya; Wang, Chuanjin; Luo, Hong
  • 46th AIAA Fluid Dynamics Conference
  • DOI: 10.2514/6.2016-4270

A Hybrid Reconstructed Discontinuous Galerkin Method for Compressible Flows on Unstructured Grids
conference, January 2016

  • Cheng, Jian; Liu, Tiegang; Luo, Hong
  • 54th AIAA Aerospace Sciences Meeting
  • DOI: 10.2514/6.2016-1330

An Implicit Finite-Volume Method for Compressible Turbulent Multiphase Flows on Unstructured Grids
conference, June 2018

A front-tracking method for viscous, incompressible, multi-fluid flows
journal, March 1992

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