Euler equation existence, non-uniqueness and mesh converged statistics.
We review existence and non-uniqueness results for the Euler equation of fluid flow. These results are placed in the context of physical models and their solutions. Non-uniqueness is in direct conflict with the purpose of practical simulations, so that a mitigating strategy, outlined here, is important. We illustrate these issues in an examination of mesh converged turbulent statistics, with comparison to laboratory experiments.
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA Computational Science Center, Brookhaven National Laboratory, Upton, NY 11793-6000, USA.
James
J
Glimm
Los Alamos National Laboratory, NM 87545, USA.
David H
DH
Sharp
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA hyulim@ams.sunysb.edu.
Hyunkyung
H
Lim
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.
Ryan
R
Kaufman
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.
Wenlin
W
Hu
Euler equations; existence; large eddy simulations; non-uniqueness