Oscillatory Behavior of Finite Difference Methods for the Solution of the Two Dimensional Transient Heat (Diffusion) Equation.
Abstract
The two dimensional transient heat (diffusion) equation with Dirichlet boundary conditions was solved using the Dufort-Frankel, Saul'ev, and, Exponential (Power-law) finite fidderence schemes. All methods were investigated for oscillatory behavior and comparisons of accuracy made. To predict the time step at which oscillatory behavior would occur, the coefficient, matrix, and probabilistic methods of stability analysis were utilized. At time steps greater than the square of the mesh divided by the thermal diffusivity, oscillatory solutions were apparent in both the Dufort-Frankel and Saul'ev schems. The exponential method, as predicted, did not oscillate for any size time step. Although the exponential scheme was the most accurate at large time steps, the solution still contained enough error to be unusable in many engineering applications. At small time steps, all methods were more accurate than the fully implicit formulation. The exponential method was found to be the slowest computationally. The Saul'ev scheme proved to be the fastest while still achieving the required degree of accuracy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1986
- Accession Number
- ADA172785
Entities
People
- Joseph E. Cuthrell
Organizations
- Air Force Institute of Technology