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Numerical Shock Propagation Using Geometrical Shock Dynamics


Schwendeman, Donald William (1986) Numerical Shock Propagation Using Geometrical Shock Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Q5VX-AF72.


Various numerical schemes are developed to calculate the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics. The basic numerical scheme is used to study the propagation of two-dimensional shock waves along walls and in channels, and the self-focusing of initially curved shock- fronts. This scheme is extended to treat shock wave motion in non-uniform media. The extended scheme is used to examine shock wave refraction at both planar and curved interfaces separating gases with different properties. Precursor-irregular refraction patterns are obtained using geometrical shock dynamics. A general numerical scheme designed to propagate a shock surface in three dimensions is presented. Three-dimensional shock focusing and shock propagation in a curved pipe are considered primarily to demonstrate the use of the three-dimensional numerical scheme. The reflection of planar shock waves from curved walls is studied. The motion of the shock is determined using the combined theories of regular reflection and geometrical shock dynamics. A numerical scheme based on the combined theories is discussed. The numerical scheme is used to calculate the reflection and subsequent focusing of weak planar shock waves. Some of the present results are compared with other solutions to the equations of geometrical shock dynamics obtained using different methods. Recent experimental investigations are discussed and compared with our results calculated using geometrical shock dynamics.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Whitham, Gerald Beresford
Thesis Committee:
  • Whitham, Gerald Beresford (chair)
  • Keller, Herbert Bishop
  • Lorenz, Jens
  • Sturtevant, Bradford
  • Ahrens, Thomas J.
Defense Date:30 April 1986
Funding AgencyGrant Number
Department of Energy (DOE)DE-AM03-76SR00767
Office of Naval Research (ONR)N00014-75-C-0702
Record Number:CaltechETD:etd-03082008-083041
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:899
Deposited By: Imported from ETD-db
Deposited On:14 Mar 2008
Last Modified:21 Dec 2019 03:54

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PDF (Schwendeman_dw_1986.pdf) - Final Version
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