Euler equation existence, non-uniqueness and mesh converged statistics

James Glimm; David H Sharp; Hyunkyung Lim; Ryan Kaufman; Wenlin Hu

doi:10.1098/rsta.2014.0282

Euler equation existence, non-uniqueness and mesh converged statistics

Philos Trans A Math Phys Eng Sci. 2015 Sep 13;373(2050):20140282. doi: 10.1098/rsta.2014.0282.

Authors

James Glimm¹, David H Sharp², Hyunkyung Lim³, Ryan Kaufman⁴, Wenlin Hu⁴

Affiliations

¹ 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.
² Los Alamos National Laboratory, NM 87545, USA.
³ Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA hyulim@ams.sunysb.edu.
⁴ Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.

Abstract

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.

Keywords: Euler equations; existence; large eddy simulations; non-uniqueness.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.