SPECTRAL VISCOSITY

A collection of selected references on

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




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

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

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

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

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  • E. Tadmor
    Essentially non-oscillatory spectral viscosity approximations
    in "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..

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

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

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

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

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

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  • Oyvind Andreassen, Carl Erik Wasberg, David C. Fritts and Joseph R. Isler
    Gravity wave breaking in two and three dimensions 1. Model description and comparison of two-dimensional evolutions
    Journal of Geophysical Research 99(D4) (1994) 8095-8108.

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  • David C. Fritts, Joseph R. Isler and Oyvind Andreassen
    Gravity wave breaking in two and three dimensions 2. Three-dimensional evolution and instability structure
    Journal of Geophysical Research 99(D4) (1994) 8109�8123.

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  • C.-W Shu and P.S. Wong
    A note on the accuracy of spectral method applied to nonlinear conservation laws
    Journal of Scientific Computation 10(3) (1995) 357-369.

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

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  • I. Lie
    On the spectral viscosity method in multi-domain Chebyshev discretizations
    in "ICOSAHOM '95", Proceedings of the Third International Conference on Spectral and High-Order Methods (A. V. Ilin and L. R. Scott, eds.), Department of Mathematics, University of Houston, TX (1996).

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  • Scientific Computation Division, NCAR
    Spectral element filters
    Annual Scientific Report (1997).

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  • B. Wingate
    Passive advection test problem
    LANL technical report (1997).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  • D. Gottlieb and S. Gottlieb
    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) 65-72..

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  • E. Tadmor and J. Tanner
    An adaptive order Godunov type central scheme
    in "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 9th International Conference in Pasadena in 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 871-880..

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  • M. H. Carpenter, D. Gottlieb and C.-W. Shu
    On the conservation and convergence to weak solutions of global schemes
    Journal of Scientific Computing 18(1) (2003) 111-132.

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

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

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

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  • R. Pasquetti
    Spectral vanishing viscosity method for LES: sensitivity to the SVV control parameters
    Journal of Turbulence 6(12) (2005).

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  • J.-L Guermond and S. Prudhomme
    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.

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  • Marcus Calhoun-Lopez and Max D. Gunzburger
    A finite element, multi-resolution viscosity method for hyperbolic conservation laws
    SIAM J. Numerical ANalysis 43(5) (2005) 1988–2011.

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  • A. Oberai and J. Wanderer
    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.

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

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  • R. Pasquetti
    Spectral vanishing viscosity method for high-order LES: computation of the dissipation rates
    in "European Conference on Computational Fluid Dynamics", ECCOMAS CFD 2006 (P. Wesseling, E. Onate and J. Periaux , eds.), TU Delft, The Netherlands (2006).

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

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

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  • T. Hou and R. Li
    Computing nearly singular solutions using pseudo-spectral methods
    Journalof Computational Physics 226 (2007) 370-397.

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  • R. Pasquetti, E. Severac, E. Serre, P. Bontoux and M. Schafer
    From stratified wakes to rotor-stator flows by an SVV-LES method
    Theoretical & Commputational Fluid dynamics 22(3-4) (2007) 261-273.

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  • A. A. Oberai, C. E. Colosqui and J. Wanderer
    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.

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  • Joel Avrin
    The Asymptotic Finite-dimensional Character of a Spectrally-hyperviscous Model of 3D Turbulent Flow
    J. Dynamics and Differntial Equations 20(2) (2008) 479-518.

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  • J. Aguirre and J. Rivas
    A spectral viscosity method based on Hermite functions for nonlinear conservation laws
    SIAM J. Numer. Anal. 46-2 (2008) 1060-1078.

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  • Daniel Castaño Díez, Max Gunzburger and Angela Kunoth
    An adaptive wavelet viscosity method for hyperbolic conservation laws
    Numerical Methods for PDEs 24(6) (2008) 1388-1404.

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  • Jean-Luc Guermond and Richard Pasquetti
    Entropy-based nonlinear viscosity for Fourier approximations of conservation laws
    C. R. Acad. Sci. Paris, Ser. I 346 (2008) 801-806.

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  • M. Minguez, R. Pasquetti and E. Serre
    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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  • Joel Avrin and Chang Xiao
    Convergence of Galerkin solutions and continuous dependence on data in spectrally hyperviscous models of 3D turbulent flow
    Journal of Differential Equations 247 (2009) 2778-2798.

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  • Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea and Xiaoming Wang
    Analysis of nonlinear spectral eddy-viscosity models of turbulence
    J. Scientific Computing 45 (2009) 294–332.

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  • Joel Avrin and Chang Xiao
    The spectrally hyper-viscous Navier-Stokes equations
    in "Transport and Mixing in Complex and Turbulent Flows", IMA poster presentation (2010).

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  • E. Serre
    High-order direct and large eddy simulations of turbulent flows in rotating cavities
    ERCOFTAC Series, 1, Direct and Large-Eddy Simulation VIII, Part 7 15(7) (2011) 405-412.

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  • Jean-Luc Guermond and Richard Pasquetti
    Entropy viscosity method for high-order approximations of conservation laws
    in "Spectral and High Order Methods for Partial Differential Equations (ICOSAHOM)", Lecture Notes in computational Science and Engineering, Vol. 76 (Jan S. Hesthaven and Einar M. Ronquist, eds.), Springer, Trondheim, Norway, June 2009 (2011) 411-418..

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  • Eunjung Lee and Max D. Gunzburger
    A finite element, filtered eddy-viscosity method for the Navier-Stokes equations with large Reynolds number
    in "KSIAM 2011 Spring Conference", http://ksiam.org/old/conference/annual111/ in 2011, Daejeon, Korea (2011).

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  • S. S. Ray, U. Frisch, S. Nazarenko and T. Matsumuto
    Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations
    Phys. Rev. E 84 (2011).

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  • L. Biancofiore, F.Gallaire and R. Pasquetti
    Influence of confinement on obstacle-free turbulent wakes
    Computers & Fluids (2012).

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  • Eitan Tadmor and Knut Waagan
    Adaptive Spectral Viscosity for hyperbolic conservation laws
    SIAM J. Scientific Computation 34(2) (2012) 993-1009.

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  • M. Gunzburger
    Multiscale spectral viscosity discretization methods for the Navier-Stokes equations
    , (or another explicit filtering turbulence model; another tweak of Smagorinsky), in "Multiscale Numerics for the Atmosphere and Ocean", Newton Institute Seminar (2012).

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  • S. Cifani and E. R. Jakobsen
    On the spectral vanishing viscosity method for periodic fractional conservation laws
    Math. Comp. 82 (2013), 1489-1514 82 (2013) 1489-1514.

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  • J. Avrin and X. Chang
    Convergence results for a class of spectrally hyperviscous models of 3-D turbulent flow
    Journal of Mathematical Analysis and Applications 409 (2013) 742-751.

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  • X. Luo
    Spectral viscosity method with generalized Hermite functions and its spectral filter for nonlinear conservation laws.

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  • Claude Bardos and Eitan Tadmor
    Stability and spectral convergence of Fourier method for nonlinear problems: on the shortcomings of the 2/3 de-aliasing method
    Numerische Mathematik (2014).

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  • S. Lanthaler and S. Mishra
    Computation of measure valued solutions for the incompressible Euler equations
    Mathematical Models and Methods in Applied Sciences (2015).

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