A Comparison Study of the Eigenvalue Method for the Solution of the Transient Heat Conduction Equation.
Abstract
This is a comparison study of the abilities of the eigenvalue method as a numerical method in solving the transient heat conduction equation. The eigenvalue method was compared to five other numerical methods; Runge-Kutta, Gears, extrapolation, fully implicit, and Crank-Nicolson. These methods were used to solved three physical problems. The first is a two dimensional slap which takes advantage of the symmetry of the problem. The second is a the same slap problem without taking advantage of the symmetry. And the third is a cylindrical problem taking full advantage of symmetry. The scope of the study is to see which methods take less computer time while maintaining sufficient accuracy. The time it takes the computer to totally execute the program was used as the time comparison basis. The accuracy is a comparison of the exact solution to the numerical solution. a root mean square average off all the grid points per time step is used. The results of the study were surprising. The accuracy of the eigenvalue method is not any better than that of the Crank-Nicolson method. The computer times show that the eigenvalue is not the fastest for short transient times. A long transient problem with nonlinear terms was not used in this study.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1986
- Accession Number
- ADA174153
Entities
People
- David B. Gee
Organizations
- Air Force Institute of Technology