Summary
The large scale motion of two-dimensional interfacial instabilities — namely the Kelvin-Helmholtz instability and the instability of a transonic jet — is examined. The numerical calculations are based on the direct simulation of the instabilities. The two-dimensional Euler equations are solved by a high resolution scheme. The movement of the interfaces is visualized by a marker particle algorithm. The interfaces are advected in a Lagrangean fashion according to the Eulerian flow field. It is shown that the numerical dissipation has a stabilizing effect similar to physical viscosity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BIRKHOFF, G.: Helmholtz and Taylor instability, in Hydrodynamic Instability, G. Birkhoff, R. Bellmann, C. C. Lin (Eds.), AMS 1962.
COLELLA, P., GLAZ, H.M.: Efficient solution algorithms for the Riemann problem for real gases, J.Comput.Phys 59 (1985), 264–289.
COLELLA, P., WOODWARD P.R.: The piecewise parabolic method (PPM) for gas dynamical simulation, J.Comput.Phys. 54 (1984) 174–201.
DYKE, M.van: An Album of Fluid Motion, Parabolic Press, Stanford, California 1982.
EINFELDT, B.: On Godunov-type methods for gas dynamics, SIAM J.Numer. Anal. 25 (1988).
HARTEN, A., LAX, P.D., LEER, B.van: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, Comm.Pure Appl.Math. 30 (1977), 611–638.
KRASNY, R.: Desingularization of periodic vortex sheet roll-up, to appear in J.Comput.Phys.
LEER, B.van: On the relation between the upwind-differencing schemes of Godunov, Engquist- Osher and Roe, SIAM J.Sci. Stat.Comput. 5 (1984), 1–21.
LEER, B.van: Towards the ultimate conservative difference scheme V. A second- order sequel to Godunov’s method, J.Comput.Phys.32 (1979) 101–136.
MUNZ, C.-D.: On the numerical dissipation of high resolution schemes for hyperbolic conservation laws, to appear in J.Comput.Phys. 1988.
MUNZ, C.-D., Schmidt, L.: Direkte numerische Simulation von Kelvin-Helmholtz Instabilitäten in kompressiblen Strömungen, to appear in ZAMM.
ROE, P.L.: Approximate Riemann solvers, parameter vectors and difference schemes, J.Comput.Phys. 43 (1981), 357–372.
STRANG, G.: On the construction and comparison of difference schemes, SIAM J.Numer.Anal.5 (1986), 506–517.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Professor Martensen on the occasion of his 60th birthday.
Rights and permissions
Copyright information
© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this chapter
Cite this chapter
Munz, CD., Schmidt, L. (1989). Numerical Simulations of Compressible Hydrodynamic Instabiltities with High Resolution Schemes. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_45
Download citation
DOI: https://doi.org/10.1007/978-3-322-87869-4_45
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-08098-3
Online ISBN: 978-3-322-87869-4
eBook Packages: Springer Book Archive