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Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

Published online by Cambridge University Press:  09 December 2009

R. M. J. KRAMER ,
D. I. PULLIN ,
D. I. MEIRON  and
C. PANTANO
R. M. J. KRAMER*
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, MC 205-45, Pasadena, CA 91125, USA
D. I. PULLIN
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, MC 205-45, Pasadena, CA 91125, USA
D. I. MEIRON
Affiliation:
Applied and Computational Mathematics, California Institute of Technology, MC 205-45, Pasadena, CA 91125, USA
C. PANTANO
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
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Abstract

The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models.

JFM classification

Mathematical Foundations: Computational methods Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 421 - 443
Copyright
Copyright © Cambridge University Press 2009

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References

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