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Accurate methods for computing inviscid and viscous Kelvin-Helmholtz instability


Chen, MJ and Forbes, LK, Accurate methods for computing inviscid and viscous Kelvin-Helmholtz instability , Journal of Computational Physics, 230, (4) pp. 1499-1515. ISSN 0021-9991 (2011) [Refereed Article]

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DOI: doi:10.1016/


The Kelvin–Helmholtz instability is modelled for inviscid and viscous fluids. Here, two bounded fluid layers flow parallel to each other with the interface between them growing in an unstable fashion when subjected to a small perturbation. In the various configurations of this problem, and the related problem of the vortex sheet, there are several phenomena associated with the evolution of the interface; notably the formation of a finite time curvature singularity and the ‘roll-up’ of the interface. Two contrasting computational schemes will be presented. A spectral method is used to follow the evolution of the interface in the inviscid version of the problem. This allows the interface shape to be computed up to the time that a curvature singularity forms, with several computational difficulties overcome to reach that point. A weakly compressible viscous version of the problem is studied using finite difference techniques and a vorticity-streamfunction formulation. The two versions have comparable, but not identical, initial conditions and so the results exhibit some differences in timing. By including a small amount of viscosity the interface may be followed to the point that it rolls up into a classic ‘cat’s-eye’ shape. Particular attention was given to computing a consistent initial condition and solving the continuity equation both accurately and efficiently.

Item Details

Item Type:Refereed Article
Keywords:Kelvin–Helmholtz instability, Inviscid fluids, Viscous fluids, Spectral methods, ADI methods, Vorticity-streamfunction, Roll-up
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Chen, MJ (Mr Michael Chen)
UTAS Author:Forbes, LK (Professor Larry Forbes)
ID Code:68720
Year Published:2011
Web of Science® Times Cited:18
Deposited By:Mathematics and Physics
Deposited On:2011-03-18
Last Modified:2018-03-05

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