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Volumn 267, Issue , 2014, Pages 176-195

Optimization-based limiters for the spectral element method

Author keywords

Finite element method; High order; Limiters; Local extrema diminishing; Mimetic; Monotone; Spectral element method

Indexed keywords

ADVECTION; CONSTRAINT THEORY; DEGREES OF FREEDOM (MECHANICS);

EID: 84896522325     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2014.02.029     Document Type: Article
Times cited : (40)

References (44)
  • 1
    • 0024917277 scopus 로고
    • Spectral element methods for the incompressible Navier-Stokes equations
    • ASME, New York, A.K. Noor, J.T. Oden (Eds.)
    • Maday Y., Patera A.T. Spectral element methods for the incompressible Navier-Stokes equations. State of the Art Surveys on Computational Mechanics 1987, 71-143. ASME, New York. A.K. Noor, J.T. Oden (Eds.).
    • (1987) State of the Art Surveys on Computational Mechanics , pp. 71-143
    • Maday, Y.1    Patera, A.T.2
  • 2
    • 0030640666 scopus 로고    scopus 로고
    • The spectral element method for the shallow water equations on the sphere
    • Taylor M., Tribbia J., Iskandarani M. The spectral element method for the shallow water equations on the sphere. J. Comput. Phys. 1997, 130:92-108.
    • (1997) J. Comput. Phys. , vol.130 , pp. 92-108
    • Taylor, M.1    Tribbia, J.2    Iskandarani, M.3
  • 3
    • 0035971808 scopus 로고    scopus 로고
    • A spectral element shallow water model on spherical geodesic grids
    • Giraldo F.X. A spectral element shallow water model on spherical geodesic grids. Int. J. Numer. Methods Fluids 2001, 35:869-901.
    • (2001) Int. J. Numer. Methods Fluids , vol.35 , pp. 869-901
    • Giraldo, F.X.1
  • 4
    • 1842735938 scopus 로고    scopus 로고
    • The spectral element atmosphere model (SEAM): High-resolution parallel computation and localized resolution of regional dynamics
    • Fournier A., Taylor M., Tribbia J. The spectral element atmosphere model (SEAM): High-resolution parallel computation and localized resolution of regional dynamics. Mon. Weather Rev. 2004, 132:726-748.
    • (2004) Mon. Weather Rev. , vol.132 , pp. 726-748
    • Fournier, A.1    Taylor, M.2    Tribbia, J.3
  • 5
    • 1842587745 scopus 로고    scopus 로고
    • A scalable spectral element Eulerian atmospheric model (SEE-AM) for NWP: Dynamical core tests
    • Giraldo F.X., Rosmond T.E. A scalable spectral element Eulerian atmospheric model (SEE-AM) for NWP: Dynamical core tests. Mon. Weather Rev. 2004, 132:133-153.
    • (2004) Mon. Weather Rev. , vol.132 , pp. 133-153
    • Giraldo, F.X.1    Rosmond, T.E.2
  • 6
    • 27144503810 scopus 로고    scopus 로고
    • Semi-implicit time-integrators for a scalable spectral element atmospheric model
    • Giraldo F.X. Semi-implicit time-integrators for a scalable spectral element atmospheric model. Q. J. R. Meteorol. Soc. 2005, 131:2431-2454.
    • (2005) Q. J. R. Meteorol. Soc. , vol.131 , pp. 2431-2454
    • Giraldo, F.X.1
  • 7
    • 23844527361 scopus 로고    scopus 로고
    • The NCAR spectral element climate dynamical core: Semi-implicit Eulerian formulation
    • Thomas S., Loft R. The NCAR spectral element climate dynamical core: Semi-implicit Eulerian formulation. J. Sci. Comput. 2005, 25:307-322.
    • (2005) J. Sci. Comput. , vol.25 , pp. 307-322
    • Thomas, S.1    Loft, R.2
  • 9
    • 85190129576 scopus 로고    scopus 로고
    • Naval Research Laboratory Spectral Element Atmospheric Model (NSEAM)
    • A sensitivity study of the Kelvin wave and the Madden-Julian oscillation in aqua-planet simulations
    • Y.J. Kim, F.X. Giraldo, M. Flatau, C.S. Liou, M.S. Peng, A sensitivity study of the Kelvin wave and the Madden-Julian oscillation in aqua-planet simulations by the Naval Research Laboratory Spectral Element Atmospheric Model (NSEAM), Journal of Geophysical Research 113.
    • Journal of Geophysical Research 113.
    • Kim, Y.J.1    Giraldo, F.X.2    Flatau, M.3    Liou, C.S.4    Peng, M.S.5
  • 12
    • 0036558652 scopus 로고    scopus 로고
    • Wind driven circulation of the Mediterranean sea simulated with a spectral element ocean model
    • Molcard A., Pinardi N., Iskandarani M., Haidvogel D. Wind driven circulation of the Mediterranean sea simulated with a spectral element ocean model. Dyn. Atmos. Ocean. 2002, 35:97-130.
    • (2002) Dyn. Atmos. Ocean. , vol.35 , pp. 97-130
    • Molcard, A.1    Pinardi, N.2    Iskandarani, M.3    Haidvogel, D.4
  • 13
    • 0036252025 scopus 로고    scopus 로고
    • Spectral-element simulations of global seismic wave propagation-I. validation
    • Komatitsch D., Tromp J. Spectral-element simulations of global seismic wave propagation-I. validation. Geophys. J. Int. 2002, 149:390-412.
    • (2002) Geophys. J. Int. , vol.149 , pp. 390-412
    • Komatitsch, D.1    Tromp, J.2
  • 19
    • 14744303015 scopus 로고    scopus 로고
    • Comparison of advection schemes for high-order hp finite element and finite volume methods
    • Iskandarani M., Levin J., Choi B.J., Haidvogel D. Comparison of advection schemes for high-order hp finite element and finite volume methods. Ocean Model. 2005, 10:233-252.
    • (2005) Ocean Model. , vol.10 , pp. 233-252
    • Iskandarani, M.1    Levin, J.2    Choi, B.J.3    Haidvogel, D.4
  • 21
    • 0003733595 scopus 로고    scopus 로고
    • Finite Volume Methods for Hyperbolic Problems
    • Cambridge University Press
    • LeVeque R. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics 2002, Cambridge University Press.
    • (2002) Cambridge Texts in Applied Mathematics
    • LeVeque, R.1
  • 22
    • 85028878087 scopus 로고    scopus 로고
    • Emerging numerical methods for atmospheric modeling
    • Springer, Berlin, Heidelberg, New York, P.H. Lauritzen, C. Jablonowski, M.A. Taylor, R.D. Nair (Eds.) Numerical Techniques for Global Atmospheric Models
    • Nair R., Levy M., Lauritzen P. Emerging numerical methods for atmospheric modeling. Lecture Notes in Computational Science and Engineeering 2011, vol. 80:251-311. Springer, Berlin, Heidelberg, New York. P.H. Lauritzen, C. Jablonowski, M.A. Taylor, R.D. Nair (Eds.).
    • (2011) Lecture Notes in Computational Science and Engineeering , vol.80 , pp. 251-311
    • Nair, R.1    Levy, M.2    Lauritzen, P.3
  • 23
    • 0037137999 scopus 로고    scopus 로고
    • Flux correction tools for finite elements
    • Kuzmin D., Turek S. Flux correction tools for finite elements. J. Comput. Phys. 2002, 175(2):525-558.
    • (2002) J. Comput. Phys. , vol.175 , Issue.2 , pp. 525-558
    • Kuzmin, D.1    Turek, S.2
  • 24
    • 10444225545 scopus 로고    scopus 로고
    • Preserving positivity for hyperbolic PDEs using variable-order finite elements with bounded polynomials
    • Berzins M. Preserving positivity for hyperbolic PDEs using variable-order finite elements with bounded polynomials. Appl. Numer. Math. 2005, 52(2-3):197-217.
    • (2005) Appl. Numer. Math. , vol.52 , Issue.2-3 , pp. 197-217
    • Berzins, M.1
  • 25
    • 0029167632 scopus 로고
    • Positive schemes and shock modelling for compressible flows
    • Jameson A. Positive schemes and shock modelling for compressible flows. Int. J. Numer. Methods Fluids 1995, 20:743-776.
    • (1995) Int. J. Numer. Methods Fluids , vol.20 , pp. 743-776
    • Jameson, A.1
  • 26
    • 77953620703 scopus 로고    scopus 로고
    • A compatible and conservative spectral element method on unstructured grids
    • Taylor M.A., Fournier A. A compatible and conservative spectral element method on unstructured grids. J. Comput. Phys. 2010, 229:5879-5895.
    • (2010) J. Comput. Phys. , vol.229 , pp. 5879-5895
    • Taylor, M.A.1    Fournier, A.2
  • 27
    • 80053904673 scopus 로고    scopus 로고
    • Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
    • Zhang X., Shu C.-W. Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Proc. R. Soc. A, Math. Phys. Eng. Sci. 2011, 467(2134):2752-2776.
    • (2011) Proc. R. Soc. A, Math. Phys. Eng. Sci. , vol.467 , Issue.2134 , pp. 2752-2776
    • Zhang, X.1    Shu, C.-W.2
  • 28
    • 77956913688 scopus 로고    scopus 로고
    • A class of deformational flow test cases for linear transport problems on the sphere
    • Nair R.D., Lauritzen P.H. A class of deformational flow test cases for linear transport problems on the sphere. J. Comput. Phys. 2010, 229(23):8868-8887.
    • (2010) J. Comput. Phys. , vol.229 , Issue.23 , pp. 8868-8887
    • Nair, R.D.1    Lauritzen, P.H.2
  • 29
    • 84874859457 scopus 로고    scopus 로고
    • A standard test case suite for two-dimensional linear transport on the sphere
    • Lauritzen P.H., Skamarock W.C., Prather M.J., Taylor M.A. A standard test case suite for two-dimensional linear transport on the sphere. Geosci. Model Dev. 2012, 5(3):887-901.
    • (2012) Geosci. Model Dev. , vol.5 , Issue.3 , pp. 887-901
    • Lauritzen, P.H.1    Skamarock, W.C.2    Prather, M.J.3    Taylor, M.A.4
  • 31
    • 70149113092 scopus 로고    scopus 로고
    • Dynamically adaptive spectral-element simulations of 2d incompressible Navier-Stokes vortex decays
    • Fournier A., Rosenberg D., Pouquet A. Dynamically adaptive spectral-element simulations of 2d incompressible Navier-Stokes vortex decays. Geophys. Astrophys. Fluid Dyn. 2009, 103(2):245-268.
    • (2009) Geophys. Astrophys. Fluid Dyn. , vol.103 , Issue.2 , pp. 245-268
    • Fournier, A.1    Rosenberg, D.2    Pouquet, A.3
  • 32
    • 0001118530 scopus 로고    scopus 로고
    • A new class of optimal high-order strong-stability-preserving time discretization methods
    • Spiteri R.J., Ruuth S.J. A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 2002, 40(2):469-491. 10.1137/S0036142901389025.
    • (2002) SIAM J. Numer. Anal. , vol.40 , Issue.2 , pp. 469-491
    • Spiteri, R.J.1    Ruuth, S.J.2
  • 33
    • 70149116587 scopus 로고    scopus 로고
    • A non-oscillatory advection operator for the compatible spectral element method
    • Springer, Berlin/Heidelberg, Computational Science ICCS 2009 Part II
    • Taylor M., St.-Cyr A., Fournier A. A non-oscillatory advection operator for the compatible spectral element method. Lect. Notes Comput. Sci. 2009, vol. 5545:273-282. Springer, Berlin/Heidelberg.
    • (2009) Lect. Notes Comput. Sci. , vol.5545 , pp. 273-282
    • Taylor, M.1    Cyr St., A.2    Fournier, A.3
  • 35
    • 85190113663 scopus 로고    scopus 로고
    • http://school.maths.uwa.edu.au/berwin/software/quadprog.html.
  • 36
    • 0020826623 scopus 로고
    • A numerically stable dual method for solving strictly convex quadratic programs
    • Goldfarb D., Idnani A. A numerically stable dual method for solving strictly convex quadratic programs. Math. Program. 1983, 27:1-33. 10.1007/BF02591962.
    • (1983) Math. Program. , vol.27 , pp. 1-33
    • Goldfarb, D.1    Idnani, A.2
  • 37
    • 84877132945 scopus 로고    scopus 로고
    • Fast optimization-based conservative remap of scalar fields through aggregate mass transfer
    • Bochev P., Ridzal D., Shashkov M. Fast optimization-based conservative remap of scalar fields through aggregate mass transfer. J. Comput. Phys. 2013, 246:37-57. 10.1016/j.jcp.2013.03.040.
    • (2013) J. Comput. Phys. , vol.246 , pp. 37-57
    • Bochev, P.1    Ridzal, D.2    Shashkov, M.3
  • 39
    • 18544381244 scopus 로고    scopus 로고
    • A discontinuous Galerkin transport scheme on the cubed-sphere
    • Nair R.D., Thomas S., Loft R. A discontinuous Galerkin transport scheme on the cubed-sphere. Mon. Weather Rev. 2005, 133:814-828.
    • (2005) Mon. Weather Rev. , vol.133 , pp. 814-828
    • Nair, R.D.1    Thomas, S.2    Loft, R.3
  • 40
    • 72449122767 scopus 로고    scopus 로고
    • A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
    • Lauritzen P.H., Nair R.D., Ullrich P.A. A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J. Comput. Phys. 2010, 229(5):1401-1424.
    • (2010) J. Comput. Phys. , vol.229 , Issue.5 , pp. 1401-1424
    • Lauritzen, P.H.1    Nair, R.D.2    Ullrich, P.A.3
  • 41
    • 84867946286 scopus 로고    scopus 로고
    • A nonoscillatory discontinuous Galerkin transport scheme on the cubed sphere
    • Zhang Y., Nair R. A nonoscillatory discontinuous Galerkin transport scheme on the cubed sphere. Mon. Weather Rev. 2012, 140:3106-3126.
    • (2012) Mon. Weather Rev. , vol.140 , pp. 3106-3126
    • Zhang, Y.1    Nair, R.2
  • 42
    • 0001906210 scopus 로고
    • A comparative study of computational methods in cosmic gas dynamics
    • van Albada G., van Leer B., Roberts W.R. A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 1982, 108(1):76-84.
    • (1982) Astron. Astrophys. , vol.108 , Issue.1 , pp. 76-84
    • van Albada, G.1    van Leer, B.2    Roberts, W.R.3
  • 43
    • 85190133181 scopus 로고    scopus 로고
    • Positivity preserving and maximum principle satisfying discontinuous Galerkin method for advection, unpublished result.
    • A. St.-Cyr, S. Blaise, A. Sandu, D. Hall, Positivity preserving and maximum principle satisfying discontinuous Galerkin method for advection, unpublished result.
    • Cyr St., A.1    Blaise, S.2    Sandu, A.3    Hall, D.4
  • 44
    • 0030452194 scopus 로고    scopus 로고
    • A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates
    • Rančić M., Purser R., Mesinger F. A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates. Q. J. R. Meteorol. Soc. 1996, 122:959-982.
    • (1996) Q. J. R. Meteorol. Soc. , vol.122 , pp. 959-982
    • Rančić, M.1    Purser, R.2    Mesinger, F.3


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