Error Prediction for the Implicit Numerical Solution of the Heat Conduction Equation
Technical publication, Sep 1966-Sep 1968
NEVADA UNIV RENO
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The results of an investigation of time- and space-truncation errors inherent in the implicit numerical analysis of the heat conduction equation are presented. Curves showing the percentage of error as a function of Biot and Fourier number for both step-function and ramp-function boundary conditions are given. Acceleration techniques, over-relaxation, and a direct tridiagonal matrix solution are presented. Methods are developed for automatic determination and printout of spatial- and time-truncation error, for extending ramp-function responses for either analytical or numerical solutions, and for synthesizing ramps of different slopes from a given transient response. An automatic time- step generator that maintains a specified error level is described and coded. Preliminary studies correlating the delta first derivative with spatial-truncation error, and accelerating the solution of a three-dimensional implicit transient solution through the use of a one-dimensional approach are given.