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Title: An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1548525
Grant/Contract Number:  
AC02-05CH11231; FA9550-15-1-0010
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Name: Journal of Computational Physics Journal Volume: 365 Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Zahr, M. J., and Persson, P. -O. An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.03.029.
Zahr, M. J., & Persson, P. -O. An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions. United States. https://doi.org/10.1016/j.jcp.2018.03.029
Zahr, M. J., and Persson, P. -O. Sun . "An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions". United States. https://doi.org/10.1016/j.jcp.2018.03.029.
@article{osti_1548525,
title = {An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions},
author = {Zahr, M. J. and Persson, P. -O.},
abstractNote = {},
doi = {10.1016/j.jcp.2018.03.029},
journal = {Journal of Computational Physics},
number = C,
volume = 365,
place = {United States},
year = {2018},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2018.03.029

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Cited by: 3 works
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Works referenced in this record:

pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization
journal, May 2011

  • Perez, Ruben E.; Jansen, Peter W.; Martins, Joaquim R. R. A.
  • Structural and Multidisciplinary Optimization, Vol. 45, Issue 1
  • DOI: 10.1007/s00158-011-0666-3

Discontinuous Galerkin solution of the Navier–Stokes equations on deformable domains
journal, April 2009

  • Persson, P. -O.; Bonet, J.; Peraire, J.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 17-20
  • DOI: 10.1016/j.cma.2009.01.012

Uniformly high order accurate essentially non-oscillatory schemes, III
journal, August 1987


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


An optimization-based framework for anisotropic simplex mesh adaptation
journal, September 2012


A Problem-Independent Limiter for High-Order Runge–Kutta Discontinuous Galerkin Methods
journal, May 2001

  • Burbeau, A.; Sagaut, P.; Bruneau, Ch. -H.
  • Journal of Computational Physics, Vol. 169, Issue 1
  • DOI: 10.1006/jcph.2001.6718

A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization: A DISTORTION TO VALIDATE AND GENERATE CURVED MESHES ON CAD SURFACES
journal, December 2015

  • Gargallo-Peiró, A.; Roca, X.; Peraire, J.
  • International Journal for Numerical Methods in Engineering, Vol. 106, Issue 13
  • DOI: 10.1002/nme.5162

Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
journal, March 2004


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

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition
journal, August 1998


Fully implicit shock tracking
journal, November 1982


On maximum-principle-satisfying high order schemes for scalar conservation laws
journal, May 2010


An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems
journal, December 2016


Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981


An adaptive least-squares method for the compressible Euler equations
journal, December 1999


A Conservative Shock Fitting Method on Unstructured Grids
journal, July 1996

  • Trépanier, J. -Y.; Paraschivoiu, M.; Reggio, M.
  • Journal of Computational Physics, Vol. 126, Issue 2
  • DOI: 10.1006/jcph.1996.0147

Sub‐cell shock capturing and spacetime discontinuity tracking for nonlinear conservation laws
journal, July 2008

  • Palaniappan, J.; Miller, S. T.; Haber, R. B.
  • International Journal for Numerical Methods in Fluids, Vol. 57, Issue 9
  • DOI: 10.1002/fld.1850

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
journal, April 2011

  • Fidkowski, Krzysztof J.; Darmofal, David L.
  • AIAA Journal, Vol. 49, Issue 4
  • DOI: 10.2514/1.J050073

SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
journal, January 2002

  • Gill, Philip E.; Murray, Walter; Saunders, Michael A.
  • SIAM Journal on Optimization, Vol. 12, Issue 4
  • DOI: 10.1137/S1052623499350013

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics
journal, March 2016


Self adjusting grid methods for one-dimensional hyperbolic conservation laws
journal, May 1983


Weighted Essentially Non-oscillatory Schemes
journal, November 1994

  • Liu, Xu-Dong; Osher, Stanley; Chan, Tony
  • Journal of Computational Physics, Vol. 115, Issue 1
  • DOI: 10.1006/jcph.1994.1187

Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations
journal, December 2002

  • Hartmann, Ralf; Houston, Paul
  • Journal of Computational Physics, Vol. 183, Issue 2
  • DOI: 10.1006/jcph.2002.7206

Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
journal, April 2008


Adaptive grid generation by minimizing residuals
journal, January 2002

  • Roe, Philip; Nishikawa, Hiroaki
  • International Journal for Numerical Methods in Fluids, Vol. 40, Issue 1-2
  • DOI: 10.1002/fld.336

Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
journal, January 2011

  • Klöckner, A.; Warburton, T.; Hesthaven, J. S.
  • Mathematical Modelling of Natural Phenomena, Vol. 6, Issue 3
  • DOI: 10.1051/mmnp/20116303

A modified artificial viscosity approach for compressible turbulence simulations
journal, August 2009


Sequential quadratic programming for large-scale nonlinear optimization
journal, December 2000


Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
journal, January 2005


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

A posteriori error estimation in finite element analysis
journal, March 1997

  • Ainsworth, Mark; Oden, J. Tinsley
  • Computer Methods in Applied Mechanics and Engineering, Vol. 142, Issue 1-2
  • DOI: 10.1016/S0045-7825(96)01107-3

High-order CFD methods: current status and perspective: HIGH-ORDER CFD METHODS
journal, January 2013

  • Wang, Z. J.; Fidkowski, Krzysztof; Abgrall, Rémi
  • International Journal for Numerical Methods in Fluids, Vol. 72, Issue 8
  • DOI: 10.1002/fld.3767

Efficient Implementation of Weighted ENO Schemes
journal, June 1996

  • Jiang, Guang-Shan; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 126, Issue 1
  • DOI: 10.1006/jcph.1996.0130

A discontinuoushp finite element method for the Euler and Navier-Stokes equations
journal, September 1999


Steady shock tracking and Newton's method applied to one-dimensional duct flow
journal, February 1981


Steady Shock Tracking, Newton’s Method, and the Supersonic Blunt Body Problem
journal, June 1982

  • Shubin, G. R.; Stephens, A. B.; Glaz, H. M.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 3, Issue 2
  • DOI: 10.1137/0903009

Algebraic Mesh Quality Metrics
journal, January 2001


Multidimensional Least Squares Fluctuation Distribution Schemes with Adaptive Mesh Movement for Steady Hyperbolic Equations
journal, January 2002

  • Baines, M. J.; Leary, S. J.; Hubbard, M. E.
  • SIAM Journal on Scientific Computing, Vol. 23, Issue 5
  • DOI: 10.1137/S1064827500370202

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

  • VonNeumann, J.; Richtmyer, R. D.
  • Journal of Applied Physics, Vol. 21, Issue 3
  • DOI: 10.1063/1.1699639

Conservative Front Tracking with Improved Accuracy
journal, January 2003

  • Glimm, James; Li, Xiaolin; Liu, Yingjie
  • SIAM Journal on Numerical Analysis, Vol. 41, Issue 5
  • DOI: 10.1137/S0036142901388627