Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods

Details Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods

2007-11-14

arxiv.org/abs/0711.2284v1

Physics

Fluid Dynamics

Euler equations: 250 years on

Scientific paper

10.1016/j.physd.2007.11.006

The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods. Based on this comparison, a Kida-Pelz like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given. This estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective.

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