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An exact Riemann-solver-based solution for regular shock refraction

Published online by Cambridge University Press:  25 May 2009

P. DELMONT ,
R. KEPPENS  and
B. VAN DER HOLST
P. DELMONT*
Affiliation:
Centre for Plasma Astrophysics, K.U. Leuven, 3001 Heverlee, Belgium Leuven Mathematical Modeling and Computational Science Centre, 3001 Heverlee, Belgium
R. KEPPENS
Affiliation:
Centre for Plasma Astrophysics, K.U. Leuven, 3001 Heverlee, Belgium Leuven Mathematical Modeling and Computational Science Centre, 3001 Heverlee, Belgium Astronomical Institute, Utrecht University, 3584 Utrecht, The Netherlands FOM institute for Plasma Physics Rijnhuizen, 3434 Nieuwegein, The Netherlands
B. VAN DER HOLST
Affiliation:
Centre for Space Environment Modeling, Ann Arbor, MI 48103, USA
*
†Email address for correspondence: peter.delmont@wis.kuleuven.be
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Abstract

We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts, and in the hydrodynamical case three signals arise. Regular refraction means that these signals meet at a single point, called the triple point. After reflection from the top wall, the contact discontinuity becomes unstable due to local Kelvin–Helmholtz instability, causing the contact surface to roll up and develop the Richtmyer–Meshkov instability (RMI). We present an exact Riemann-solver-based solution strategy to describe the initial self-similar refraction phase, by which we can quantify the vorticity deposited on the contact interface. We investigate the effect of a perpendicular magnetic field and quantify how its addition increases the deposition of vorticity on the contact interface slightly under constant Atwood number. We predict wave-pattern transitions, in agreement with experiments, von Neumann shock refraction theory and numerical simulations performed with the grid-adaptive code AMRVAC. These simulations also describe the later phase of the RMI.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 33 - 53
Copyright
Copyright © Cambridge University Press 2009

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References

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