TY - JOUR
T1 - Numerical solutions for the one-dimensional heat-conduction equation using a spreadsheet
AU - Gvirtzman, Zohar
AU - Garfunkel, Zvi
PY - 1996/12
Y1 - 1996/12
N2 - We show how to use a spreadsheet to calculate numerical solutions of the one-dimensional time-dependent heat-conduction equation. We find the spreadsheet to be a practical tool for numerical calculations, because the algorithms can be implemented simply and quickly without complicated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mathematical operations. We implement the explicit and the Crank-Nicholson forms of the finite-difference approximations and discuss the geological applications of both methods. We also show how to adjust these two algorithms to a nonhomogeneous lithosphere in which the thermal properties (thermal conductivity, density, and radioactive heat generation) change from the upper crust to the lower crust and to the mantle. The solution is presented in a way that can fit any spreadsheet (Lotus-123, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macros that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix.
AB - We show how to use a spreadsheet to calculate numerical solutions of the one-dimensional time-dependent heat-conduction equation. We find the spreadsheet to be a practical tool for numerical calculations, because the algorithms can be implemented simply and quickly without complicated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mathematical operations. We implement the explicit and the Crank-Nicholson forms of the finite-difference approximations and discuss the geological applications of both methods. We also show how to adjust these two algorithms to a nonhomogeneous lithosphere in which the thermal properties (thermal conductivity, density, and radioactive heat generation) change from the upper crust to the lower crust and to the mantle. The solution is presented in a way that can fit any spreadsheet (Lotus-123, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macros that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix.
KW - Basin analysis
KW - Crank-Nicholson
KW - Explicit
KW - Finite-difference methods
KW - Heat conduction
KW - Spreadsheet
KW - Thermal modeling
UR - http://www.scopus.com/inward/record.url?scp=0030391145&partnerID=8YFLogxK
U2 - 10.1016/S0098-3004(96)00052-0
DO - 10.1016/S0098-3004(96)00052-0
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AN - SCOPUS:0030391145
SN - 0098-3004
VL - 22
SP - 1147
EP - 1158
JO - Computers and Geosciences
JF - Computers and Geosciences
IS - 10
ER -