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arXiv · 1803.06893

On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem

Philipp W. Schroeder·Volker John·Philip L. Lederer·Christoph Lehrenfeld·Gert Lube·Joachim Schöberl
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Abstract

Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.

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BibTeXRIS

Philipp W. Schroeder, Volker John, Philip L. Lederer, Christoph Lehrenfeld, Gert Lube, Joachim Schöberl. 2018-03-19. On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem. https://doi.org/10.1016/j.camwa.2018.10.030

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