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Simulation of Richtmyer-Meshkov Flows for Elastic-Plastic Solids in Planar and Converging Geometries Using an Eulerian Framework


Lopez Ortega, Alejandro (2013) Simulation of Richtmyer-Meshkov Flows for Elastic-Plastic Solids in Planar and Converging Geometries Using an Eulerian Framework. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4WJ6-D795.


This thesis presents a numerical and analytical study of two problems of interest involving shock waves propagating through elastic-plastic media: the motion of converging (imploding) shocks and the Richtmyer-Meshkov (RM) instability. Since the stress conditions encountered in these cases normally produce large deformations in the materials, an Eulerian description, in which the spatial coordinates are fixed, is employed. This formulation enables a direct comparison of similarities and differences between the present study of phenomena driven by shock-loading in elastic-plastic solids, and in fluids, where they have been studied extensively. In the first application, Whitham's shock dynamics (WSD) theory is employed for obtaining an approximate description of the motion of an elastic-plastic material processed by a cylindrically/spherically converging shock. Comparison with numerical simulations of the full set of equations of motion reveal that WSD is an accurate tool for characterizing the evolution of converging shocks at all stages. The study of the Richtmyer-Meshkov flow (i.e., interaction between the interface separating two materials of different density and a shock wave incoming at an angle) in solids is performed by means of analytical models for purely elastic solids and numerical simulations when plasticity is included in the material model. To this effect, an updated version of a previously developed multi-material, level-set-based, Eulerian framework for solid mechanics is employed. The revised code includes the use of a multi-material HLLD Riemann problem for imposing material boundary conditions, and a new formulation of the equations of motion that makes use of the stretch tensor while avoiding the degeneracy of the stress tensor under rotation. Results reveal that the interface separating two elastic solids always behaves in a stable oscillatory or decaying oscillatory manner due to the existence of shear waves, which are able to transport the initial vorticity away from the interface. In the case of elastic-plastic materials, the interface behaves at first in an unstable manner similar to a fluid. Ejecta formation is appreciated under certain initial conditions while in other conditions, after an initial period of growth, the interface displays a quasi-stationary long-term behavior due to stress relaxation. The effect of secondary shock-interface interactions (re-shocks) in converging geometries is also studied. A turbulent mixing zone, similar to what is observed in gas--gas interfaces, is created, especially when materials with low strength driven by moderate to strong shocks are considered.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:compressible flows; computational fluid and solid mechanics; Eulerian description of material motion; ; Richtmyer-Meshkov instability; converging shocks
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Awards:William F. Ballhaus Prize, 2013. Kalam Prize for Aerospace Engineering, 2009.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pullin, Dale Ian (advisor)
  • Meiron, Daniel I. (co-advisor)
Thesis Committee:
  • Pullin, Dale Ian (chair)
  • Meiron, Daniel I.
  • Ortiz, Michael
  • Ravichandran, Guruswami
  • Bruno, Oscar P.
Defense Date:15 February 2013
Non-Caltech Author Email:alejandro_lopez_ortega (AT)
Funding AgencyGrant Number
National Nuclear Security AdminstrationDE-FC52-08NA28613
Projects:Predictive Science Academic Alliance Program
Record Number:CaltechTHESIS:02202013-185004693
Persistent URL:
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Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7488
Deposited By: Alejandro Lopez Ortega
Deposited On:26 Apr 2013 22:32
Last Modified:03 Oct 2019 23:59

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