On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem
| Autor: | Volker John, Philip L. Lederer, Joachim Schöberl, Gert Lube, Philipp W. Schroeder, Christoph Lehrenfeld |
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| Rok vydání: | 2019 |
| Předmět: |
FOS: Physical sciences
010103 numerical & computational mathematics 01 natural sciences Instability symbols.namesake FOS: Mathematics Mathematics - Numerical Analysis Sensitivity (control systems) 0101 mathematics Mathematics Computer simulation Turbulence Fluid Dynamics (physics.flu-dyn) Reynolds number Numerical Analysis (math.NA) Physics - Fluid Dynamics Mechanics Computational Physics (physics.comp-ph) 16. Peace & justice Finite element method 010101 applied mathematics Computational Mathematics Computational Theory and Mathematics Modeling and Simulation Pairing symbols Compressibility Physics - Computational Physics |
| Zdroj: | Computers & Mathematics with Applications. 77:1010-1028 |
| ISSN: | 0898-1221 |
| Popis: | 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. 24 pages, 12 figures, 2 tables |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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