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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ftdtic:ADA006581 2023-05-15T16:37:14+02:00 Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. Takagi,Shunsuke COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER N H 1975-02 text/html http://www.dtic.mil/docs/citations/ADA006581 http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA006581 en eng http://www.dtic.mil/docs/citations/ADA006581 APPROVED FOR PUBLIC RELEASE DTIC AND NTIS Snow Ice and Permafrost Theoretical Mathematics *ICE *APPROXIMATION(MATHEMATICS) *SPLINES WATER MATRICES(MATHEMATICS) FREEZING NUMERICAL INTEGRATION PARTIAL DIFFERENTIAL EQUATIONS *Spline approximation Galerkin method Glaciology Text 1975 ftdtic 2016-02-20T09:17:22Z 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. Text Ice Ice Sheet permafrost Defense Technical Information Center: DTIC Technical Reports database Nicholson ENVELOPE(78.236,78.236,-68.612,-68.612) |
institution |
Open Polar |
collection |
Defense Technical Information Center: DTIC Technical Reports database |
op_collection_id |
ftdtic |
language |
English |
topic |
Snow Ice and Permafrost Theoretical Mathematics *ICE *APPROXIMATION(MATHEMATICS) *SPLINES WATER MATRICES(MATHEMATICS) FREEZING NUMERICAL INTEGRATION PARTIAL DIFFERENTIAL EQUATIONS *Spline approximation Galerkin method Glaciology |
spellingShingle |
Snow Ice and Permafrost Theoretical Mathematics *ICE *APPROXIMATION(MATHEMATICS) *SPLINES WATER MATRICES(MATHEMATICS) FREEZING NUMERICAL INTEGRATION PARTIAL DIFFERENTIAL EQUATIONS *Spline approximation Galerkin method Glaciology Takagi,Shunsuke Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
topic_facet |
Snow Ice and Permafrost Theoretical Mathematics *ICE *APPROXIMATION(MATHEMATICS) *SPLINES WATER MATRICES(MATHEMATICS) FREEZING NUMERICAL INTEGRATION PARTIAL DIFFERENTIAL EQUATIONS *Spline approximation Galerkin method Glaciology |
description |
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. |
author2 |
COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER N H |
format |
Text |
author |
Takagi,Shunsuke |
author_facet |
Takagi,Shunsuke |
author_sort |
Takagi,Shunsuke |
title |
Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
title_short |
Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
title_full |
Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
title_fullStr |
Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
title_full_unstemmed |
Spline Approximation to the Freezing of Water in a Cylindrical Hole Drilled in an Ice Sheet. |
title_sort |
spline approximation to the freezing of water in a cylindrical hole drilled in an ice sheet. |
publishDate |
1975 |
url |
http://www.dtic.mil/docs/citations/ADA006581 http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA006581 |
long_lat |
ENVELOPE(78.236,78.236,-68.612,-68.612) |
geographic |
Nicholson |
geographic_facet |
Nicholson |
genre |
Ice Ice Sheet permafrost |
genre_facet |
Ice Ice Sheet permafrost |
op_source |
DTIC AND NTIS |
op_relation |
http://www.dtic.mil/docs/citations/ADA006581 |
op_rights |
APPROVED FOR PUBLIC RELEASE |
_version_ |
1766027531895439360 |