The interaction of shock waves with fluid interfaces

Authors:
John Grove
Affiliations:
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 USA
Venue:
Advances in Applied Mathematics
Year:
1989

Citing 0
Cited 6

Spherical Richtmyer-Meshkov instability for axisymmetric flow

Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
Analytic solutions of unstable interfaces for all density ratios in axisymmetric flows

Journal of Computational and Applied Mathematics
Analytic solutions of unstable interfaces for all density ratios in axisymmetric flows

Journal of Computational and Applied Mathematics
A fast algorithm for moving interface problems

ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Vortex simulations of impulsivelyaccelerated unstable interface

Mathematical and Computer Modelling: An International Journal
Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

Enhanced resolution for the computation of the interaction of shock waves with fluid interfaces is achieved through a detailed mathematical analysis of 2-dimensional wave interactions produced during the collision of the waves. This computation is carried to late times, which are characterized by interface instability and chaotic mixing processes. Algorithms for incorporating the wave interaction analysis and the resulting bifurcation of front topology give an important extension of the front tracking method and are presented here. The mathematical analysis shows that the customary theory for oblique 2-dimensional wave interactions is equivalent to a 1-dimensional Riemann problem for steady (supersonic) flow. This analysis, known for polytropic gases, is extended here to a general equation of state. Moreover, the asymptotic limit of a small incident angle is analyzed to obtain a well-conditioned numerical algorithm. This limit is found to define a 1-dimensional unsteady Riemann problem.