Masters Theses

Date of Award

6-1984

Degree Type

Thesis

Degree Name

Master of Science

Major

Engineering Science

Major Professor

A. J. Baker

Abstract

The primary purpose of this study was to assess the effects of various terms in the formulation of a Newton matrix iteration Jacobian on the convergence rate of an implicit finite element algorithm for solution of the quasi—one dimensional Euler equations. An algorithm and computer code developed by A.J. Baker and M.O. Soliman was used as a basis for the study. In the original test of the algorithm only monotonic convergence was achieved. A detailed check of the algorithm derivation exposed several errors in the original formulation and the omission of several terms in the original computer code was discovered. A Riemann shock tube problem was used as the primary test case with a DeLaval nozzle used to test area dependent terms. Checking the revisions individually gave some changes in the convergence histories of the dependent variables, but no significant change in the overall convergence rate. However, when the revisions were taken collectively, quadra tic convergence was achieved with a concurrent 24% increase in efficiency. The second portion of this study was to determine the appli cability of a timestep optimization procedure to the fully revised algorithm. The optimization procedure is based on an approximately linear relationship between the size of the timestep and the maximum "Delta" values at that timestep. The optimization procedure was tested on a DeLaval nozzle operating at both subsonic and transonic conditions. The ii ili optimization procedure gave promising results when applied to smooth solutions with significant increase in computational efficiency and only minimal effects on solution accuracy. When applied to nonsmooth (shocked) solutions the optimization procedure produced poor results with decreases in efficiency or lose of convergence occurring in all test cases. These results indicate that the methods used in the optimization procedure do not model the given situation with sufficient accuracy to properly control the convergence.

Download
Files over 3MB may be slow to open. For best results, right-click and select "save as..."

Share

COinS