Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods
arXiv:0711.2284 · doi:10.1016/j.physd.2007.11.006
Abstract
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.
arXiv commentEuler equations: 250 years on
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