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Part I. The Numerical Solution of Hyperbolic Systems of Conservation Laws. Part II. Composite Overlapping Grid Techniques


Henshaw, William Douglas (1985) Part I. The Numerical Solution of Hyperbolic Systems of Conservation Laws. Part II. Composite Overlapping Grid Techniques. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/kz0y-2j77.


Part I

A method is described for the numerical solution of hyperbolic systems of conservation laws in one space dimension. The basis of the scheme is to use finite differences where the solution is smooth and the method of characteristics where the solution is not smooth. The method can accurately represent shocks. Results are presented for the solution of the equations of gas dynamics. The examples illustrate the accuracy of the method when discontinuities are present and the code's performance on difficult problems of interacting shocks and shock formation.

Part II

Techniques for the numerical solution of partial differential equations on composite overlapping meshes are discussed. Methods for the solution of time dependent and elliptic problems are illustrated, including a discussion of implicit time stepping and using the multigrid algorithm for the iterative solution of Poisson's equation. Two model problems are analyzed. The first gives insight into the accuracy of the solution to elliptic equations on overlapping meshes. The second deals with the numerical approximation of boundary conditions for vorticity stream function formulations. Computational results are presented.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Conservation laws; multigrid; overlapping grids; vorticity-stream-function
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Awards:The W. P. Carey & Co., Inc. Prize in Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kreiss, Heinz-Otto
Thesis Committee:
  • Kreiss, Heinz-Otto (chair)
  • Keller, Herbert Bishop
  • Saffman, Philip G.
  • List, E. John
  • Lorenz, Jens
Defense Date:23 May 1985
Non-Caltech Author Email:henshaw1 (AT)
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-83-K-0422
Record Number:CaltechETD:etd-03312008-100117
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1227
Deposited By: Imported from ETD-db
Deposited On:08 Apr 2008
Last Modified:16 Apr 2021 22:11

Thesis Files

PDF (Henshaw_wd_1985.pdf) - Final Version
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