Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet.

An interpolation continuous up to the first-order derivatives is needed to solve this problem, because the first-order derivatives are used in the formulation of the movement of the freezing front. The requirement is met in this paper by use of a parabolic spline. The Crank-Nicholson formula is used...

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Bibliographic Details
Main Author: Takagi,Shunsuke
Other Authors: COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER N H
Format: Text
Language:English
Published: 1975
Subjects:
Snow
Ice and Permafrost
Theoretical Mathematics
*ICE
*APPROXIMATION(MATHEMATICS)
*SPLINES
WATER
MATRICES(MATHEMATICS)
FREEZING
NUMERICAL INTEGRATION
PARTIAL DIFFERENTIAL EQUATIONS
*Spline approximation
Galerkin method
Glaciology
Nicholson
Ice
Ice Sheet
permafrost
Online Access:http://www.dtic.mil/docs/citations/ADA006581
http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA006581
Description
Summary:An interpolation continuous up to the first-order derivatives is needed to solve this problem, because the first-order derivatives are used in the formulation of the movement of the freezing front. The requirement is met in this paper by use of a parabolic spline. The Crank-Nicholson formula is used to set up the predictor-corrector scheme of time integration. Several iterations are needed to advance one step in time because of the implicit nature of the Crank-Nicholson formula and the nonlinearity involved in the freezing problem.

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