期刊
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
卷 32, 期 1, 页码 23-34出版社
SPRINGER
DOI: 10.1007/s00162-017-0434-0
关键词
Euler-Voigt; Navier-Stokes-Voigt; Inviscid regularization; Turbulence models; alpha-Models; Blow-up criterion for Euler
资金
- ONR [N00014-15-1-2333]
- NSF [DMS-1109640, DMS-1109645]
We report the results of a computational investigation of two blow-up 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 Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter . Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.
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