SPECTRAL VISCOSITY

A collection of selected references on

High-frequency wave-dependent methods
for time-dependent problems with large gradients

  • E. Tadmor (1989)
    Convergence of spectral methods for nonlinear conservation laws
    SIAM Journal Numerical Analysis 26 (1989) 30-44.

  • Y. Maday & E. Tadmor (1989)
    Analysis of the spectral vanishing viscosity method for periodic conservation laws
    SIAM Journal Numerical Analysis 26 (1989) 854-870.

  • E. Tadmor (1990)
    Shock capturing by the spectral viscosity method
    Computer Methods in Applied Mechanics and Engineering 80 (1990) 197-208.

  • S. Schochet (1990)
    The rate of convergence of spectral-viscosity methods for periodic scalar conservation laws
    SIAM Journal on Numerical Methods 27 (1990) 1142-1159.

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  • E. Tadmor (1991)
    Essentially non-oscillatory spectral viscosity approximations
    "Hyperbolic Problems - Theory, Numerical Methods and Applications", Proceedings of the 3rd International Conference on Hyperbolic Problems, Vol. II (B. Engquist and B. Gustafsson, eds.), Studentlitteratur and Chartwell-Bratt (1991), 861-873.

  • E. Tadmor (1993)
    Total variation and error estimates for spectral viscosity approximations
    Mathematics of Computation 60 (1993) 245-256.

  • E. Tadmor  (1993)
    Super viscosity and spectral approximations of nonlinear conservation laws
    "Numerical Methods for Fluid Dynamics. IV" (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford 1993, pp. 69-82.

  • Y. Maday. S. Ould-Kaber & E. Tadmor (1993)
    Legendre pseudospectral viscosity method for nonlinear conservation laws
    SIAM Journal of Numerical Analysis 30 (1993) 321-342.

  • G.-Q Chen, Q. Du  & E. Tadmor (1993)
    Spectral viscosity approximations to multidimensional scalar conservation laws
    Mathematics of Computation 61 (1993) 629-643.

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  • I. Lie  (1994) gzipped file
    On the spectral viscosity method in multi-domain Chebyshev discretizations

  • O. Andreassen, I. Lie & C. E. Wasberg (1994) [ gzipped file]
    The spectral viscosity method applied to simulation of waves in stratified atmosphere
    Journal of Computational Physics 110(2) (1994) 257-273.

  • C.-W Shu & P.S. Wong (1995)
    A note on the accuracy of spectral method applied to nonlinear conservation laws
    Journal of Scientific Computing 10 (1995) 357-369.

  • S. M. Ould Kaber (1996)
    A Legendre pseudospectral viscosity method
    Journal of Computational Physics 128 (1996) 165-180.

  • B. Wingate (1997) [html file]
    Passive advection test problem
    LANL technical report

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  • Scientific Computation Division, NCAR[html file]
    Spectral element filters
    Annual Scientific Report (1997)

  • H.-P. Ma (1998) ]
    Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws
    SIAM Journal of Numerical Analysis 35 (1998) 869-892.

  • H.-P Ma (1998)
    Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws
    SIAM Journal of Numerical Analysis 35 (1998)  893-908.

  • N. A. Adams (1999)
    Advances in direct de-convolution modeling of subgrid-scales for flows with discontinuities
    Stanford Center for Turbulence Research (1999) 317-327.

  • H. Holden, K. H. Karlsen & H. Risebro (1999)
    Operator splitting methods for generalized Korteweg-De Vries equations
    Journal of Computational Physics 153 (1999) 203-222.

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  • O. Lepsky (2000)
    A spectral viscosity approximations to Hamilton-Jacobi equations
    SIAM Journal on Numerical analysis 38 (2000) 1439-1453.

  • A. Gelb  & E. Tadmor (2000)
    Enhanced spectral viscosity approximations for conservation laws
    Applied Numerical Mathematics 33 (2000) 3-21.

  • G.-S. Karamanos & G. E. Karniadakis (2000)
    A spectral vanishing viscosity method for large eddy-simulations
    Journal of Computational Physics 163 (2000) 22-50.

  • T. J. R. Hughes, L. Mazzei, A. A. Oberai & A. A. Wray
    The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence
    Physics of Fluids 13(2) (2001) 505-512.

  • S. Cerutti, C. Meneveau & O. Knio,
    Spectral and hyper eddy viscosity in high-Reynolds-number turbulence
    J. Fluid Mechanics 421 (2000) 307-338.

  • A. Gelb & J. Gleeson (2001)
    A spectral viscosity for shallow water equations in spherical geometry  
    Monthly Weather Review 129 (2001) 2346-2360.

  • B.-Y. Guo, H.-P. Ma & E. Tadmor (2001)
    Spectral vanishing viscosity method for nonlinear conservation laws
    SIAM Journal on Numerical Analysis 39 (2001), 1254-1268.

  • E. Tadmor & J. Tanner (2002)
    Adaptive mollifiers -- high resolution recovery of piecewise smooth data from its spectral information
    Foundations of Computational Mathematics 2(2) (2002) 155-189.

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  • N. Adams & S. Stolz (2002)
    A subgrid-scale deconvolution approach for shock capturing
    Journal of Computational Physics 178 (2002) 391-426.

  • E. Tadmor & J. Tanner (2002)
    An adaptive order Godunov type central scheme
    in ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 9th International Conference in Pasadena, Mar. 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 871-880..

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  • S. Sarra (2002)
    Chebyshev Super Spectral Viscosity method for a Two-Dimensional Fluidized Bed Model
    International Journal for Numerical Methods in Fluids 4 (2002) 1-18.

  • S. Sarra (2003)
    Chebyshev super spectral viscosity method for a fluidized bed model
    Journal of Computational Physics 186 (2003) 630-651.

  • S. Sarra (2003)
    The spectral signal processing suite
    ACM Transaction on Mathematical Software 29 (2003) 195-217.

  • W.-S. Dun, D. Gottlieb & J.-H. Jung (2003)
    A multidomain spectral method for supersonic reactive flows
    Journal of Computational Physics 192 (2003) 325-352.

  • X. Ma, V. Symeonidis & G. E. Karniadakis (2003) [abstract]
    A spectral vanishing viscosity method for stabilizing viscoelastic flows
    Journal of Non-Newtonian Fluid Mechanics 115 (2003) 125-155.

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  • D. Gottlieb & S. Gottlieb (2003)
    Spectral methods for discontinuous problems
    Proceedings of the 20th Biennial Conference on Numerical Analysis (D F Griffiths & G A Watson eds.),
    University of Dundee, 2003, pp. 65-72.

  • J.-L Guermond & S. Prudhomme (2003)
    Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
    Mathematical Modeling and Numerical Analysis 37 (2003) 893-908.

  • S. Sirisup & G. E. Karniadakis (2004)
    A spectral viscosity method for correcting the long-term behavior of POD models
    Journal of of Computational Physics 194 (2004) 92-116.

  • C. J. Xu & R. Pasquetti (2004)
    Stabilized spectral element computations of high Reynolds number incompressible flows
    J. Computational Physics 196(2) (2004) 680-704.

  • R. Pasquetti (2005)
    Spectral vanishing viscosity method for LES: sensitivity to the SVV control parameters
    Special issue: Marseille Euromech Colloquium vol. 6, N12 (2005).

  • R. Pasquetti (2005)
    High order LES modeling of turbulent incompressible flow
    C. R. Acad. Sci. (Mechanique) 333 (2005) 39-49

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  • R. Pasquetti (2006)
    Spectral vanishing viscosity method for large-eddy simulation of turbulent flow
    Journal of Scientific Computing 27 (2006) 365-375.

  • J.-L Guermond & S. Prudhomme (2005)
    On the construction of suitable solutions to the Navier&-Stokes equations and questions regarding the definition of large eddy simulation
    Physica D 207(1-2) (2005) 64-78.

  • A. Oberai & J. Wanderer(2006)
    A dynamic multiscale viscosity method for the spectral approximation of conservation laws
    Computer Methods in Applied Mechanics and Engineering 195 (13-16) (2006) 1778-1992.

  • M. Calhoun-Lopes & M. Gunzburger (2007)
    The efficient implementation of a finite-element, multi-resolution viscosity method for nonlinear conservation laws
    Journal of Computational Physics 225 (2007) 1288-1313.

  • E. Severac & E. Serre (2007)
    A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities
    Journal of Computational Physics 226 (2007) 1234-1255.

  • A. A. Oberai, C. E. Colosqui & J. Wanderer (2008)
    Analytical estimates of the subgrid model for Burgers equation: Ramifications for spectral methods for conservation laws
    International Journal for Multiscale Computational Engineering 6(4) (2008) 299-307.

  • M. Minguez, R. Pasquetti & E. Serre (2009)
    Spectral vanishing viscosity stabilized LES of the Ahmed body turbulent wake
    Communications in Computational Physics 5(2-4) (2009) 635-648.

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  • J. Avrin & C. Xiao (2009)
    Convergence of Galerkin solutions and continuous dependence on data in spectrally hyperviscous models of 3D turbulent flow
    J. Diff. Equations 247 (2009) 2778-2798.