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

Zahr, M. J.; Persson, P. -O.

doi:10.1016/j.jcp.2018.03.029

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

Journal Article · 30 June 2018 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2018.03.029 · OSTI ID:1548525

;

Not Available

View Accepted Manuscript (Publisher)

Cite

Export

Save

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231; AC02-05CH11231

OSTI ID:: 1548525

Alternate ID(s):: OSTI ID: 23124968

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 365; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (44)

Fully implicit shock tracking Bell, J. B.; Shubin, G. R.; Solomon, J. M. Journal of Computational Physics, Vol. 48, Issue 2 https://doi.org/10.1016/0021-9991(82)90048-1	journal	November 1982
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws Krivodonova, L.; Xin, J.; Remacle, J. -F. Applied Numerical Mathematics, Vol. 48, Issue 3-4 https://doi.org/10.1016/j.apnum.2003.11.002	journal	March 2004
A Problem-Independent Limiter for High-Order Runge–Kutta Discontinuous Galerkin Methods Burbeau, A.; Sagaut, P.; Bruneau, Ch. -H. Journal of Computational Physics, Vol. 169, Issue 1 https://doi.org/10.1006/jcph.2001.6718	journal	May 2001
Conservative Front Tracking with Improved Accuracy Glimm, James; Li, Xiaolin; Liu, Yingjie SIAM Journal on Numerical Analysis, Vol. 41, Issue 5 https://doi.org/10.1137/S0036142901388627	journal	January 2003
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics Fidkowski, Krzysztof J.; Darmofal, David L. AIAA Journal, Vol. 49, Issue 4 https://doi.org/10.2514/1.J050073	journal	April 2011
An optimization-based framework for anisotropic simplex mesh adaptation Yano, Masayuki; Darmofal, David L. Journal of Computational Physics, Vol. 231, Issue 22 https://doi.org/10.1016/j.jcp.2012.06.040	journal	September 2012
Steady Shock Tracking, Newton’s Method, and the Supersonic Blunt Body Problem Shubin, G. R.; Stephens, A. B.; Glaz, H. M. SIAM Journal on Scientific and Statistical Computing, Vol. 3, Issue 2 https://doi.org/10.1137/0903009	journal	June 1982
Self adjusting grid methods for one-dimensional hyperbolic conservation laws Harten, Ami; Hyman, James M. Journal of Computational Physics, Vol. 50, Issue 2 https://doi.org/10.1016/0021-9991(83)90066-9	journal	May 1983
pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization Perez, Ruben E.; Jansen, Peter W.; Martins, Joaquim R. R. A. Structural and Multidisciplinary Optimization, Vol. 45, Issue 1 https://doi.org/10.1007/s00158-011-0666-3	journal	May 2011
A Method for the Numerical Calculation of Hydrodynamic Shocks VonNeumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, Issue 3 https://doi.org/10.1063/1.1699639	journal	March 1950
Weighted Essentially Non-oscillatory Schemes Liu, Xu-Dong; Osher, Stanley; Chan, Tony Journal of Computational Physics, Vol. 115, Issue 1 https://doi.org/10.1006/jcph.1994.1187	journal	November 1994
On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics Wheatley, V.; Kumar, H.; Huguenot, P. Journal of Computational Physics, Vol. 229, Issue 3 https://doi.org/10.1016/j.jcp.2009.10.003	journal	February 2010
Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver Biros, George; Ghattas, Omar SIAM Journal on Scientific Computing, Vol. 27, Issue 2 https://doi.org/10.1137/S106482750241565X	journal	January 2005
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo SIAM Journal on Numerical Analysis, Vol. 39, Issue 5 https://doi.org/10.1137/S0036142901384162	journal	January 2002
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
An adaptive least-squares method for the compressible Euler equations Taghaddosi, F.; Habashi, W. G.; Guèvremont, G. International Journal for Numerical Methods in Fluids, Vol. 31, Issue 7 https://doi.org/10.1002/(SICI)1097-0363(19991215)31:7<1121::AID-FLD913>3.0.CO;2-R	journal	December 1999
Steady shock tracking and Newton's method applied to one-dimensional duct flow Shubin, G. R.; Stephens, A. B.; Glaz, H. M. Journal of Computational Physics, Vol. 39, Issue 2 https://doi.org/10.1016/0021-9991(81)90157-1	journal	February 1981
Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang Journal of Computational Physics, Vol. 227, Issue 9 https://doi.org/10.1016/j.jcp.2007.12.024	journal	April 2008
Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations Hartmann, Ralf; Houston, Paul Journal of Computational Physics, Vol. 183, Issue 2 https://doi.org/10.1006/jcph.2002.7206	journal	December 2002
Multidimensional Least Squares Fluctuation Distribution Schemes with Adaptive Mesh Movement for Steady Hyperbolic Equations Baines, M. J.; Leary, S. J.; Hubbard, M. E. SIAM Journal on Scientific Computing, Vol. 23, Issue 5 https://doi.org/10.1137/S1064827500370202	journal	January 2002
On maximum-principle-satisfying high order schemes for scalar conservation laws Zhang, Xiangxiong; Shu, Chi-Wang Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2009.12.030	journal	May 2010
A posteriori error estimation in finite element analysis Ainsworth, Mark; Oden, J. Tinsley Computer Methods in Applied Mechanics and Engineering, Vol. 142, Issue 1-2 https://doi.org/10.1016/S0045-7825(96)01107-3	journal	March 1997
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V Cockburn, Bernardo; Shu, Chi-Wang Journal of Computational Physics, Vol. 141, Issue 2 https://doi.org/10.1006/jcph.1998.5892	journal	April 1998
Discontinuous Galerkin solution of the Navier–Stokes equations on deformable domains Persson, P. -O.; Bonet, J.; Peraire, J. Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 17-20 https://doi.org/10.1016/j.cma.2009.01.012	journal	April 2009
A modified artificial viscosity approach for compressible turbulence simulations Bhagatwala, Ankit; Lele, Sanjiva K. Journal of Computational Physics, Vol. 228, Issue 14 https://doi.org/10.1016/j.jcp.2009.04.009	journal	August 2009
Adaptive grid generation by minimizing residuals Roe, Philip; Nishikawa, Hiroaki International Journal for Numerical Methods in Fluids, Vol. 40, Issue 1-2 https://doi.org/10.1002/fld.336	journal	January 2002
An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems Zahr, M. J.; Persson, P. -O. Journal of Computational Physics, Vol. 326 https://doi.org/10.1016/j.jcp.2016.09.012	journal	December 2016
Sequential quadratic programming for large-scale nonlinear optimization Boggs, Paul T.; Tolle, Jon W. Journal of Computational and Applied Mathematics, Vol. 124, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00429-5	journal	December 2000
High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition Zhong, Xiaolin Journal of Computational Physics, Vol. 144, Issue 2 https://doi.org/10.1006/jcph.1998.6010	journal	August 1998
A simple shock-capturing technique for high-order discontinuous Galerkin methods: A SIMPLE SHOCK-CAPTURING TECHNIQUE FOR HIGH-ORDER DG METHODS Huerta, A.; Casoni, E.; Peraire, J. International Journal for Numerical Methods in Fluids, Vol. 69, Issue 10 https://doi.org/10.1002/fld.2654	journal	August 2011
Uniformly high order accurate essentially non-oscillatory schemes, III Harten, Ami; Engquist, Bjorn; Osher, Stanley Journal of Computational Physics, Vol. 71, Issue 2 https://doi.org/10.1016/0021-9991(87)90031-3	journal	August 1987
A decade of progress on anisotropic mesh adaptation for computational fluid dynamics Alauzet, Frédéric; Loseille, Adrien Computer-Aided Design, Vol. 72 https://doi.org/10.1016/j.cad.2015.09.005	journal	March 2016
Sub‐cell shock capturing and spacetime discontinuity tracking for nonlinear conservation laws Palaniappan, J.; Miller, S. T.; Haber, R. B. International Journal for Numerical Methods in Fluids, Vol. 57, Issue 9 https://doi.org/10.1002/fld.1850	journal	July 2008
A discontinuoushp finite element method for the Euler and Navier-Stokes equations Baumann, Carlos Erik; Oden, J. Tinsley International Journal for Numerical Methods in Fluids, Vol. 31, Issue 1 https://doi.org/10.1002/(SICI)1097-0363(19990915)31:1<79::AID-FLD956>3.0.CO;2-C	journal	September 1999
A Conservative Shock Fitting Method on Unstructured Grids Trépanier, J. -Y.; Paraschivoiu, M.; Reggio, M. Journal of Computational Physics, Vol. 126, Issue 2 https://doi.org/10.1006/jcph.1996.0147	journal	July 1996
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 Gargallo-Peiró, A.; Roca, X.; Peraire, J. International Journal for Numerical Methods in Engineering, Vol. 106, Issue 13 https://doi.org/10.1002/nme.5162	journal	December 2015
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization Gill, Philip E.; Murray, Walter; Saunders, Michael A. SIAM Journal on Optimization, Vol. 12, Issue 4 https://doi.org/10.1137/S1052623499350013	journal	January 2002
High-order CFD methods: current status and perspective: HIGH-ORDER CFD METHODS Wang, Z. J.; Fidkowski, Krzysztof; Abgrall, Rémi International Journal for Numerical Methods in Fluids, Vol. 72, Issue 8 https://doi.org/10.1002/fld.3767	journal	January 2013
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
Finite Volume Methods for Hyperbolic Problems LeVeque, Randall J. https://doi.org/10.1017/CBO9780511791253	book	January 2002
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method Klöckner, A.; Warburton, T.; Hesthaven, J. S. Mathematical Modelling of Natural Phenomena, Vol. 6, Issue 3 https://doi.org/10.1051/mmnp/20116303	journal	January 2011
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters Qiu., Jianxian; Shu, Chi-Wang SIAM Journal on Scientific Computing, Vol. 26, Issue 3 https://doi.org/10.1137/S1064827503425298	journal	January 2005
Algebraic Mesh Quality Metrics Knupp, Patrick M. SIAM Journal on Scientific Computing, Vol. 23, Issue 1 https://doi.org/10.1137/S1064827500371499	journal	January 2001

Similar Records

Third-order semi-discrete central scheme for conservation laws andconvection-diffusion equations

Journal Article · 1999 · SIAM Journal on Scientific Computing · OSTI ID:893721

Kurganov, Alexander; Levy, Doron

On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws

Journal Article · 2017 · International Journal of High Performance Computing Applications · OSTI ID:1860892

Loffeld, J.; Hittinger, J. A. F.

A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations

Journal Article · 1997 · Journal of Computational Physics · OSTI ID:494292

Bassi, F; Rebay, S

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

Citation Formats

References (44)

Similar Records

Related Subjects