Some results on uniformly high-order accurate essentially nonoscillatory schemes
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Shock capturing by the spectral viscosity method
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Family of spectral filters for discontinuous problems
Journal of Scientific Computing
Legendre pseudospectral viscosity method for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Performance of under-resolved two-dimensional incompressible flow simulations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Conservative high-order finite-difference schemes for low-Mach number flows
Journal of Computational Physics
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
High Order Schemes for Resolving Waves: Number of Points per Wavelength
Journal of Scientific Computing
On spurious vortical structures
Journal of Computational Physics
Journal of Computational Physics
On the Conservation and Convergence to Weak Solutions of Global Schemes
Journal of Scientific Computing
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Spectral properties of high-order residual-based compact schemes for unsteady compressible flows
Journal of Computational Physics
WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows
Journal of Computational Physics
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A spectral method and a fifth-order weighted essentially non-oscillatory method were used to examine the consequences of filtering in the numerical simulation of the three-dimensional evolution of nearly-incompressible, inviscid Taylor--Green vortex flow. It was found that numerical filtering using the high-order exponential filter and low-pass filter with sharp high mode cutoff applied in the spectral simulations significantly affects the convergence of the numerical solution. While the conservation property of the spectral method is highly desirable for fluid flows described by a system of hyperbolic conservation laws, spectral methods can yield erroneous results and conclusions at late evolution times when the flow eventually becomes under-resolved. In particular, it is demonstrated that the enstrophy and kinetic energy, which are two integral quantities often used to evaluate the quality of numerical schemes, can be misleading and should not be used unless one can assure that the solution is sufficiently well-resolved. In addition, it is shown that for the Taylor--Green vortex (for example) it is useful to compare the predictions of at least two numerical methods with different algorithmic foundations (such as a spectral and finite-difference method) in order to corroborate the conclusions from the numerical solutions when the analytical solution is not known.