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

Citation

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. https://resolver.caltech.edu/CaltechETD:etd-03312008-100117

Abstract

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.

Thesis Files