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 -