Spectral Viscosity method (Eitan Tadmor)

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.
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.
E. Tadmor Shock capturing by the spectral viscosity method Computer Methods in Applied Mechanics and Engineering 80 (1990) 197-208.
S. Schochet The rate of convergence of spectral-viscosity methods for periodic scalar conservation laws SIAM Journal of Numerical Analysis 27 (1990) 1142-1159.
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..
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.), Clarendon Press, Oxford (1993) 69-82..
E. Tadmor Total variation and error estimates for spectral viscosity approximations Mathematics of Computation 60 (1993) 245-256.
G.-Q Chen, Q. Du and E. Tadmor Spectral viscosity approximations to multidimensional scalar conservation laws Mathematics of Computation 61 (1993) 629-643.
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.
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.
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.
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.
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.
S. M. Ould Kaber A Legendre pseudospectral viscosity method Journal of Computational Physics 128 (1996) 165-180.
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).
Scientific Computation Division, NCAR Spectral element filters Annual Scientific Report (1997).
B. Wingate Passive advection test problem LANL technical report (1997).
H.-P. Ma Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws SIAM Journal of Numerical Analysis 35 (1998) 869-892.
H.-P. Ma Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws SIAM Journal of Numerical Analysis 35 (1998) 893-908.
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.
N. A. Adams Advances in direct de-convolution modeling of subgrid-scales for flows with discontinuities Stanford Center for Turbulence Research (1999) 317-327.
A. Gelb and E. Tadmor Enhanced spectral viscosity approximations for conservation laws Applied Numerical Mathematics 33 (2000) 3-21.
S. Cerutti, C. Meneveau and O. Knio Spectral and hyper eddy viscosity in high-Reynolds-number turbulence J. Fluid Mechanics 421 (2000) 307-338.
G.-S. Karamanos and G. E. Karniadakis A spectral vanishing viscosity method for large eddy-simulations Journal of Computational Physics 163 (2000) 22-50.
O. Lepsky A spectral viscosity approximations to Hamilton-Jacobi equations SIAM Journal of Numerical Analysis 38 (2000) 1439-1453.
A. Gelb and J. Gleeson A spectral viscosity for shallow water equations in spherical geometry Monthly Weather Review 129 (2001) 2346-2360.
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.
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.
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.
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.
N. Adams and S. Stolz A subgrid-scale deconvolution approach for shock capturing Journal of Computational Physics 178 (2002) 391-426.
S. Sarra The spectral signal processing suite ACM Transaction on Mathematical Software 29 (2003) 195-217.
S. Sarra Chebyshev super spectral viscosity method for a fluidized bed model Journal of Computational Physics 186 (2003) 630-651.
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.
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.
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.
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..
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..
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.
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.
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.
J.-L. Guermond, J. T. Oden and S. Prudhomme Mathematical perspectives on large eddy simulation models for turbulent flows Journal of Mathematical Fluid Mechanics 6(2) (2004) 194-248.
R. Pasquetti High order LES modeling of turbulent incompressible flow C. R. Acad. Sci. (Mechanique) 333 (2005) 39-49.
R. Pasquetti Spectral vanishing viscosity method for LES: sensitivity to the SVV control parameters Journal of Turbulence 6(12) (2005).
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.
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.
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.
R. Pasquetti Spectral vanishing viscosity method for large-eddy simulation of turbulent flow Journal of Scientific Computing 27 (2006) 365-375.
Robert Kirby and Spencer Sherwin Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling Computer Methods in Applied Mechanics and Engineering 195 (23-24) (2006) 3128-3144.
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).
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.
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.
T. Hou and R. Li Computing nearly singular solutions using pseudo-spectral methods Journalof Computational Physics 226 (2007) 370-397.
E. Tadmor Filters, mollifiers and the computation of the Gibbs phenomenon Acta Numerica 16 (2007) 305-378.
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.
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.
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.
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.
Daniel Castaño Diez, Max Gunzburger and Angela Kunoth An adaptive wavelet viscosity method for hyperbolic conservation laws Numerical Methods for PDEs 24(6) (2008) 1388-1404.
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.
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.
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.
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.
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).
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.
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..
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", 2011, Daejeon, Korea (2011).
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).
L. Biancofiore, F.Gallaire and R. Pasquetti Influence of confinement on obstacle-free turbulent wakes Computers & Fluids 58 (2012) 27-44.
Eitan Tadmor and Knut Waagan Adaptive Spectral Viscosity for hyperbolic conservation laws SIAM J. Scientific Computation 34(2) (2012) 993-1009.
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).
S. Cifani and E. R. Jakobsen On the spectral vanishing viscosity method for periodic fractional conservation laws Math. Comp. 82 (2013) 1489-1514.
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.
X. Luo Spectral viscosity method with generalized Hermite functions and its spectral filter for nonlinear conservation laws.
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).
S. Lanthaler and S. Mishra Computation of measure valued solutions for the incompressible Euler equations Mathematical Models and Methods in Applied Sciences (2015).
R.C. Moura, S.J. Sherwin, J. Peiro Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosity Journal of Computational Physics 307 (2016) 401-422.
J. Avrin Asymptotic Galerkin convergence and dynamical system results for the 3-D spectrally-hyperviscous Navier-Stokes equations on bounded domains European Journal of Mathematics (2019).
Samuel Lanthaler and Siddhartha Mishra On the convergence of the spectral viscosity method for the incompressible Euler equations with rough initial data Foundations of Computational Mathematics 20 (2019) 1309-1362.
Rodrigo C. Moura, Mansoor Aman, Joaquim Peiro, Spencer J. Sherwin Spatial eigenanalysis of spectral/hp continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows Journal of Computational Physics 406 (2020) 109112.
S. Lanthaler, S. Mishra and C. Parés-Pulido Statistical solutions of the incompressible Euler equations Mathematical Models and Methods in Applied Sciences 31(2) (2021) 223-292
Philippe G. LeFloch and Hendrik Ranocha Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts Journal of Scientific Computing 87:55 (2021).
Rodrigo M. Pereira, Natacha Nguyen Van Yen, Kai Schneider, and Marie Farge Adaptive solution of initial value problems by a dynamical Galerkin scheme Multiscale Modeling & Simulation 20(3) (2022) 147-1166.

SPECTRAL VISCOSITY

A collection of selected references on

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

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