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

• 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

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.