TY - JOUR

T1 - On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

AU - Schroeder, Philipp W.

AU - John, Volker

AU - Lederer, Philip L.

AU - Lehrenfeld, Christoph

AU - Lube, Gert

AU - Schöberl, Joachim

N1 - Funding Information:
Philip L. Lederer has been funded by the Austrian Science Fund (FWF) through the research program “Taming complexity in partial differential systems” (F65) - project “Automated discretization in multiphysics” (P10).
Funding Information:
Philip L. Lederer has been funded by the Austrian Science Fund (FWF) through the research program ?Taming complexity in partial differential systems? (F65) - project ?Automated discretization in multiphysics? (P10).
Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2019/2/15

Y1 - 2019/2/15

N2 - 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.

AB - 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.

KW - Direct numerical simulation

KW - Incompressible Navier–Stokes equations

KW - Kelvin–Helmholtz instability

KW - Mixing layer

KW - Reference solutions

KW - Sensitivity with respect to components of numerical methods

UR - http://www.scopus.com/inward/record.url?scp=85056202476&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.10.030

DO - 10.1016/j.camwa.2018.10.030

M3 - Article

SN - 0898-1221

VL - 77

SP - 1010

EP - 1028

JO - Computers & mathematics with applications

JF - Computers & mathematics with applications

IS - 4

ER -