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

• Published in: Computers & mathematics with applications (1987) Vol. 77; no. 4; pp. 1010 - 1028
• Main Authors: Schroeder, Philipp W., John, Volker, Lederer, Philip L., Lehrenfeld, Christoph, Lube, Gert, Schöberl, Joachim
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.02.2019; Elsevier BV
• Subjects: Computational fluid dynamics; Computer simulation; Direct numerical simulation; Divergence; Finite element method; Fluid flow; High Reynolds number; Incompressible flow; Incompressible Navier–Stokes equations; Kelvin-Helmholtz instability; Mixing layer; Reference solutions; Reynolds number; Sensitivity; Sensitivity with respect to components of numerical methods; Stability analysis; Kelvin–Helmholtz instability; Reference solutions; Incompressible Navier–Stokes equations; Sensitivity with respect to components of numerical methods; Direct numerical simulation; Mixing layer
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2018.10.030

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.