Speaker
Description
It is well known that Nek5000/RS's spectral element method (SEM) delivers
spectacular convergence in the limit that the solution is well-resolved. Less
understood, however, is the behavior of the SEM for marginally-resolved
solutions that are frequently encountered in practice, particularly in the case
of large-eddy simulations, where the turbulence is inherently under-resolved.
We present an extensive study of 1D dispersion error for the SEM at varying
wavenumbers and varying degrees of $h$- and $p$-refinement, with the principal
parameter being the number of points per wavelength (PPW). The results
illustrate some surprising behaviors, particularly at low PPW. We put these
results into context with other studies and other discretizations, including
high-order DG, and we suggest simple error mitigation strategies that can lead
to improved performance for SEM advection in higher space dimensions.
Relevance for Nek [100 words max]
Paul
