Comparison study of the eigenvalue method for the solution of the transient heat-conduction equation. Master's thesis

Technical Report · Tue Dec 31 23:00:00 EST 1985

OSTI ID:6920849

Gee, D B

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 slab that takes advantage of the symmetry of the problem. The second is a the same slab 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.

• Research Organization: Air Force Inst. of Tech., Wright-Patterson AFB, OH (USA)
• OSTI ID: 6920849
• Report Number(s): AD-A-174153/7/XAB; AFIT/GNE/ENP-86M-6
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100 -- Nuclear Reactor Technology-- Theory & Calculation
42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
OPERATION
PARTIAL DIFFERENTIAL EQUATIONS
REACTOR OPERATION
SYMMETRY
TRANSIENTS