A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization
Abstract
We report the results of a computational investigation of two blowup criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D EulerVoigt equations, which are known to be globally wellposed. Moreover, simulations of the 3D EulerVoigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blowup criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the betterbehaved 3D EulerVoigt equations. The new criteria are only known to be suficient for blowup. Therefore, to test the robustness of the inviscidregularization approach, we also investigate analogous criteria for blowup of the 1D Burgers equation, where blowup is wellknown to occur.
 Authors:
 Univ. of Nebraska, Lincoln, NE (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Texas A & M Univ., College Station, TX (United States); Weizmann Inst. of Science, Rehovot (Israel)
 Univ. of Exeter (United Kingdom)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1357141
 Report Number(s):
 LAUR1723192
Journal ID: ISSN 09354964
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Theoretical and Computational Fluid Dynamics
 Additional Journal Information:
 Journal Volume: 32; Journal Issue: 1; Journal ID: ISSN 09354964
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics; EulerVoigt; NavierStokesVoigt; Inviscid Regularization, Turbulence Models; Inviscid Regularization; Turbulence Models
Citation Formats
Larios, Adam, Petersen, Mark R., Titi, Edriss S., and Wingate, Beth. A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization. United States: N. p., 2017.
Web. doi:10.1007/s0016201704340.
Larios, Adam, Petersen, Mark R., Titi, Edriss S., & Wingate, Beth. A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization. United States. doi:10.1007/s0016201704340.
Larios, Adam, Petersen, Mark R., Titi, Edriss S., and Wingate, Beth. Sat .
"A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization". United States.
doi:10.1007/s0016201704340. https://www.osti.gov/servlets/purl/1357141.
@article{osti_1357141,
title = {A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization},
author = {Larios, Adam and Petersen, Mark R. and Titi, Edriss S. and Wingate, Beth},
abstractNote = {We report the results of a computational investigation of two blowup criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D EulerVoigt equations, which are known to be globally wellposed. Moreover, simulations of the 3D EulerVoigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blowup criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the betterbehaved 3D EulerVoigt equations. The new criteria are only known to be suficient for blowup. Therefore, to test the robustness of the inviscidregularization approach, we also investigate analogous criteria for blowup of the 1D Burgers equation, where blowup is wellknown to occur.},
doi = {10.1007/s0016201704340},
journal = {Theoretical and Computational Fluid Dynamics},
number = 1,
volume = 32,
place = {United States},
year = {Sat Apr 29 00:00:00 EDT 2017},
month = {Sat Apr 29 00:00:00 EDT 2017}
}

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