Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Mechanics



+44 (0)20 7594 5052s.sherwin Website




313BCity and Guilds BuildingSouth Kensington Campus






BibTex format

author = {Moura, RC and Sherwin, SJ and Peiro, J},
doi = {10.1016/},
journal = {Journal of Computational Physics},
pages = {401--422},
title = {Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity},
url = {},
volume = {307},
year = {2015}

RIS format (EndNote, RefMan)

AB - This study addresses linear dispersion–diffusion analysis for the spectral/hp continuousGalerkin (CG) formulation in one dimension. First, numerical dispersion and diffusioncurves are obtained for the advection–diffusion problem and the role of multipleeigencurves peculiar to spectral/hp methods is discussed. From the eigencurves’ behaviour,we observe that CG might feature potentially undesirable non-smooth dispersion/diffusioncharacteristics for under-resolved simulations of problems strongly dominated by eitherconvection or diffusion. Subsequently, the linear advection equation augmented withspectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics ofCG with SVV-based stabilization are verified to display similar non-smooth features inflow regions where convection is much stronger than dissipation or vice-versa, owing toa dependency of the standard SVV operator on a local Péclet number. First a modificationis proposed to the traditional SVV scaling that enforces a globally constant Péclet numberso as to avoid the previous issues. In addition, a new SVV kernel function is suggestedand shown to provide a more regular behaviour for the eigencurves along with aconsistent increase in resolution power for higher-order discretizations, as measured bythe extent of the wavenumber range where numerical errors are negligible. The dissipationcharacteristics of CG with the SVV modifications suggested are then verified to be broadlyequivalent to those obtained through upwinding in the discontinuous Galerkin (DG)scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme isfound to have a slightly higher resolution power for the same dissipation levels. Theseresults show that improved CG-SVV characteristics can be pursued via different kernelfunctions with the aid of optimization algorithms.
AU - Moura,RC
AU - Sherwin,SJ
AU - Peiro,J
DO - 10.1016/
EP - 422
PY - 2015///
SN - 1090-2716
SP - 401
TI - Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity
T2 - Journal of Computational Physics
UR -
UR -
VL - 307
ER -