Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Legendre pseudospectral viscosity method for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Preserving symmetries in the proper orthogonal decomposition
SIAM Journal on Scientific Computing
The spectral viscosity method applied to simulation of waves in a stratified atmosphere
Journal of Computational Physics
A Legendre pseudospectral viscosity method
Journal of Computational Physics
Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
A spectral vanishing viscosity method for large-eddy simulations
Journal of Computational Physics
Model reduction for real-time fluids
ACM SIGGRAPH 2006 Papers
Enablers for robust POD models
Journal of Computational Physics
Modular bases for fluid dynamics
ACM SIGGRAPH 2009 papers
Reduced-order models for parameter dependent geometries based on shape sensitivity analysis
Journal of Computational Physics
Reduced order models based on local POD plus Galerkin projection
Journal of Computational Physics
Two-level discretizations of nonlinear closure models for proper orthogonal decomposition
Journal of Computational Physics
Reduced-order modeling of transonic flows around an airfoil submitted to small deformations
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Computers & Mathematics with Applications
Strong and weak constraint variational assimilations for reduced order fluid flow modeling
Journal of Computational Physics
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Local POD Plus Galerkin Projection in the Unsteady Lid-Driven Cavity Problem
SIAM Journal on Scientific Computing
Modelling and Simulation in Engineering
A numerical investigation of velocity-pressure reduced order models for incompressible flows
Journal of Computational Physics
Hi-index | 31.48 |
Low-dimensional flow dynamical systems may converge to erroneous states after long-time integration, even if they are initialized with the correct state. In this paper, we investigate the accuracy of such two-dimensional models constructed from Karhunen-Loeve expansions for flows past a circular cylinder. We first demonstrate that although the short-term dynamics may be predicted accurately with only a handful of modes retained, drifting of the solution may arise after a few hundred vortex shedding cycles. We then propose a dissipative model based on a spectral viscosity (SV) diffusion convolution operator. The parameters of the SV model are selected rigorously based on bifurcation analysis. Our results show that this is an effective way of improving the accuracy of long-term predictions of low-dimensional Galerkin systems.