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

James Glimm
, David H. Sharp
, Hyunkyung Lim
, Ryan Kaufman
, Wenlin Hu

Applied Mathematics and Statistics

Los Alamos National Laboratory
Stony Brook University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Article number	20140282
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	373
Issue number	2050
DOIs	https://doi.org/10.1098/rsta.2014.0282
State	Published - Sep 13 2015

Keywords

Euler equations
Existence
Large eddy simulations
Non-uniqueness

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10.1098/rsta.2014.0282

Cite this

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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.",

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AU - Kaufman, Ryan

AU - Hu, Wenlin

PY - 2015/9/13

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AB - 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.

KW - Euler equations

KW - Existence

KW - Large eddy simulations

KW - Non-uniqueness

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DO - 10.1098/rsta.2014.0282

M3 - Article

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JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Euler equation existence, non-uniqueness and mesh converged statistics

Abstract

Keywords

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