메뉴 건너뛰기




Volumn 228, Issue 20, 2009, Pages 7643-7661

Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations

Author keywords

Adjoint based error estimation; Compressible flow; Discontinuous Galerkin methods; High speed flow; High order methods; hp Multigrid approach; Mesh refinement; Output functional

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DEGREES OF FREEDOM (MECHANICS); ERRORS; EULER EQUATIONS; GALERKIN METHODS; MESH GENERATION;

EID: 69049085439     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.07.012     Document Type: Article
Times cited : (116)

References (32)
  • 1
    • 35648977909 scopus 로고    scopus 로고
    • Shock capturing with higher-order, PDE-based artificial viscosity
    • AIAA Paper 2007-3823, June
    • G.E. Barter, D.L. Darmofal, Shock capturing with higher-order, PDE-based artificial viscosity, AIAA Paper 2007-3823, June 2007.
    • (2007)
    • Barter, G.E.1    Darmofal, D.L.2
  • 2
    • 0031537299 scopus 로고    scopus 로고
    • High-order accurate discontinuous finite element solution of 2D Euler equations
    • Bassi F., and Rebay S. High-order accurate discontinuous finite element solution of 2D Euler equations. J. Comput. Phys. 138 (1997) 251-285
    • (1997) J. Comput. Phys. , vol.138 , pp. 251-285
    • Bassi, F.1    Rebay, S.2
  • 3
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Appl. Mech. Eng. 35 (1998) 2440-2463
    • (1998) SIAM J. Numer. Appl. Mech. Eng. , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 4
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. SIAM J. Sci. Comput. 16 (2001) 173-261
    • (2001) SIAM J. Sci. Comput. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 5
    • 18344378961 scopus 로고    scopus 로고
    • p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
    • Fidkowski K.J., Oliver T.A., Lu J., and Darmofal D. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comput. Phys. 207 (2005) 92-113
    • (2005) J. Comput. Phys. , vol.207 , pp. 92-113
    • Fidkowski, K.J.1    Oliver, T.A.2    Lu, J.3    Darmofal, D.4
  • 6
    • 26944434674 scopus 로고    scopus 로고
    • A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
    • Luo H., Baum J.D., and Lohner R. A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids. J. Comput. Phys. 211 2 (2006) 767-783
    • (2006) J. Comput. Phys. , vol.211 , Issue.2 , pp. 767-783
    • Luo, H.1    Baum, J.D.2    Lohner, R.3
  • 7
    • 31744436751 scopus 로고    scopus 로고
    • High-order discontinuous Galerkin methods using an hp-multigrid approach
    • Nastase C.R., and Mavriplis D.J. High-order discontinuous Galerkin methods using an hp-multigrid approach. J. Comput. Phys. 213 1 (2006) 330-357
    • (2006) J. Comput. Phys. , vol.213 , Issue.1 , pp. 330-357
    • Nastase, C.R.1    Mavriplis, D.J.2
  • 8
    • 35648947145 scopus 로고    scopus 로고
    • Sub-cell shock capturing for discontinuous Galerkin methods
    • AIAA Paper 2006-112, January
    • P.-O. Persson, J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods, AIAA Paper 2006-112, January 2006.
    • (2006)
    • Persson, P.-O.1    Peraire, J.2
  • 9
    • 34547522173 scopus 로고    scopus 로고
    • Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations
    • Wang L., and Mavriplis D.J. Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations. J. Comput. Phys. 225 2 (2007) 1994-2015
    • (2007) J. Comput. Phys. , vol.225 , Issue.2 , pp. 1994-2015
    • Wang, L.1    Mavriplis, D.J.2
  • 10
    • 0001164460 scopus 로고
    • A posteriori error bounds and global error control for approximation of ordinary differential equations
    • Estep D. A posteriori error bounds and global error control for approximation of ordinary differential equations. SIAM J. Numer. Anal. 32 (1995) 1-48
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1-48
    • Estep, D.1
  • 11
    • 85022001969 scopus 로고    scopus 로고
    • An optimal control approach to a posteriori error estimation in finite element methods
    • Becker R., and Rannacher R. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2002)
    • (2002) Acta Numer. , vol.10
    • Becker, R.1    Rannacher, R.2
  • 12
    • 0034352046 scopus 로고    scopus 로고
    • A posteriori error analysis for stabilised finite element approximations of transport problems
    • Houston P., Hartmann R., and Suli E. A posteriori error analysis for stabilised finite element approximations of transport problems. Comput. Methods Appl. Mech. Eng. 190 11-12 (2000) 1483-1508
    • (2000) Comput. Methods Appl. Mech. Eng. , vol.190 , Issue.11-12 , pp. 1483-1508
    • Houston, P.1    Hartmann, R.2    Suli, E.3
  • 13
    • 0036347672 scopus 로고    scopus 로고
    • hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems
    • Houston P., and Suli E. hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. SIAM J. Sci. Comput. 23 4 (2001) 1226-1252
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.4 , pp. 1226-1252
    • Houston, P.1    Suli, E.2
  • 14
    • 0037059262 scopus 로고    scopus 로고
    • Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
    • Hartmann R., and Houston P. Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. J. Comput. Phys. 183 2 (2002) 508-532
    • (2002) J. Comput. Phys. , vol.183 , Issue.2 , pp. 508-532
    • Hartmann, R.1    Houston, P.2
  • 15
    • 34547538932 scopus 로고    scopus 로고
    • A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations
    • Fidkowski K.J., and Darmofal D. A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations. J. Comput. Phys. 225 2 (2007) 1653-1672
    • (2007) J. Comput. Phys. , vol.225 , Issue.2 , pp. 1653-1672
    • Fidkowski, K.J.1    Darmofal, D.2
  • 16
    • 7244226418 scopus 로고    scopus 로고
    • Adjoint and defect error bounding and correction for functional estimates
    • Pierce N.A., and Giles M. Adjoint and defect error bounding and correction for functional estimates. J. Comput. Phys. 200 2 (2004) 769-794
    • (2004) J. Comput. Phys. , vol.200 , Issue.2 , pp. 769-794
    • Pierce, N.A.1    Giles, M.2
  • 17
    • 0037050818 scopus 로고    scopus 로고
    • Grid adaptation for functional outputs: application to two-dimensional inviscid flows
    • Venditti D.A., and Darmofal D.L. Grid adaptation for functional outputs: application to two-dimensional inviscid flows. J. Comput. Phys 176 1 (2002) 40-69
    • (2002) J. Comput. Phys , vol.176 , Issue.1 , pp. 40-69
    • Venditti, D.A.1    Darmofal, D.L.2
  • 18
    • 20344379763 scopus 로고    scopus 로고
    • Numerical Methods and Error Estimation for Conservation Laws on Structured and Unstructured Meshes
    • von Karman Institute for Fluid Dynamics, Brussels, Belgium, March
    • T. Barth, Numerical Methods and Error Estimation for Conservation Laws on Structured and Unstructured Meshes, Lecture Notes, Series: 2003-04, von Karman Institute for Fluid Dynamics, Brussels, Belgium, March 2003.
    • (2003) Lecture Notes , vol.2003 -04
    • Barth, T.1
  • 19
    • 51349114279 scopus 로고    scopus 로고
    • Adjoint-based adaptive mesh refinement for complex geometries
    • AIAA Paper 2008-725, January
    • M. Nemec, M.J. Aftosmis, M. Wintzer, Adjoint-based adaptive mesh refinement for complex geometries, AIAA Paper 2008-725, January 2008.
    • (2008)
    • Nemec, M.1    Aftosmis, M.J.2    Wintzer, M.3
  • 20
    • 10444252655 scopus 로고    scopus 로고
    • A note on the design of hp-adaptive finite element methods for elliptic partial differential equations
    • Houston P., and Suli E. A note on the design of hp-adaptive finite element methods for elliptic partial differential equations. Comput. Methods Appl. Mech. Eng. 194 2-5 (2005) 229-243
    • (2005) Comput. Methods Appl. Mech. Eng. , vol.194 , Issue.2-5 , pp. 229-243
    • Houston, P.1    Suli, E.2
  • 21
    • 0028450353 scopus 로고
    • Adaptive mesh strategies for the spectral element method
    • Mavriplis C. Adaptive mesh strategies for the spectral element method. Comput. Methods. Appl. Mech. Eng. 116 (1994) 77-86
    • (1994) Comput. Methods. Appl. Mech. Eng. , vol.116 , pp. 77-86
    • Mavriplis, C.1
  • 22
    • 1042281121 scopus 로고    scopus 로고
    • Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
    • Krivodonova L., Xin J., Remacle J.-F., Chevaugeon N., and Flaherty J. Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl. Numer. Math. 48 3 (2004) 323-338
    • (2004) Appl. Numer. Math. , vol.48 , Issue.3 , pp. 323-338
    • Krivodonova, L.1    Xin, J.2    Remacle, J.-F.3    Chevaugeon, N.4    Flaherty, J.5
  • 23
    • 0031261331 scopus 로고    scopus 로고
    • On the choice of wavespeeds for the HLLC Riemann solver
    • Batten P., Clarke N., Lambert C., and Causon D.M. On the choice of wavespeeds for the HLLC Riemann solver. SIAM J. Sci. Comput. 18 2 (1997) 1553-1570
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.2 , pp. 1553-1570
    • Batten, P.1    Clarke, N.2    Lambert, C.3    Causon, D.M.4
  • 24
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the HLL-Riemann solver
    • Toro E.F., Spruce M., and Spears W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 1 (1994) 25-34
    • (1994) Shock Waves , vol.4 , Issue.1 , pp. 25-34
    • Toro, E.F.1    Spruce, M.2    Spears, W.3
  • 25
    • 0003561264 scopus 로고    scopus 로고
    • Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
    • No. 97-65, NASA/CR-97-206253, 1997
    • C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report No. 97-65, NASA/CR-97-206253, 1997.
    • ICASE Report
    • Shu, C.-W.1
  • 29
    • 0022076980 scopus 로고
    • High degree efficient symmetrical Gaussian quadrature rules for the triangle
    • Dunavant D.A. High degree efficient symmetrical Gaussian quadrature rules for the triangle. Int. J. Numer. Meth. Eng. 21 6 (1985) 1129-1148
    • (1985) Int. J. Numer. Meth. Eng. , vol.21 , Issue.6 , pp. 1129-1148
    • Dunavant, D.A.1
  • 30
    • 0022144545 scopus 로고
    • Economical symmetrical quadrature rules for complete polynomials over a square domain
    • Dunavant D.A. Economical symmetrical quadrature rules for complete polynomials over a square domain. Int. J. Numer. Meth. Eng. 21 10 (1985) 1777-1784
    • (1985) Int. J. Numer. Meth. Eng. , vol.21 , Issue.10 , pp. 1777-1784
    • Dunavant, D.A.1
  • 31
    • 0001742674 scopus 로고    scopus 로고
    • Unstructured grid techniques
    • Mavriplis D.J. Unstructured grid techniques. Annu. Rev. Fluid. Mech. 29 1 (1997) 473-514
    • (1997) Annu. Rev. Fluid. Mech. , vol.29 , Issue.1 , pp. 473-514
    • Mavriplis, D.J.1
  • 32
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems
    • Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 2 (1998) 199-224
    • (1998) J. Comput. Phys. , vol.141 , Issue.2 , pp. 199-224
    • Cockburn, B.1    Shu, C.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.