On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets
This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumu...
Main Authors: | , |
---|---|
Language: | English |
Published: |
2006
|
Subjects: | |
Online Access: | http://cds.cern.ch/record/989975 |
id |
ftcern:oai:cds.cern.ch:989975 |
---|---|
record_format |
openpolar |
spelling |
ftcern:oai:cds.cern.ch:989975 2023-05-15T16:40:55+02:00 On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets Bueler, E Brown, J 2006-10-16 http://cds.cern.ch/record/989975 eng eng http://cds.cern.ch/record/989975 physics/0610106 oai:cds.cern.ch:989975 Other Fields of Physics 2006 ftcern 2018-07-28T08:33:44Z This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumulation and heat source functions which make a chosen pair of functions for thickness and temperature into exact solutions of the coupled system. The solution we construct here is ``TestG'' in (Bueler and others, 2006) and the steady state solution ``Test F'' is a special case. In the second section we give a reference C implementation of these exact solutions. In the last section we give an error analysis of a finite difference scheme for the temperature equation in the thermocoupled model. The error analysis gives three results, first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for stability of the advection scheme, second an equation for error growth which contributes to understanding the famous ``spokes'' of (Payne and others, 2000), and third a convergence theorem under stringent fixed geometry and smoothness assumptions. Other/Unknown Material Ice Sheet CERN Document Server (CDS) Payne ENVELOPE(167.867,167.867,-72.817,-72.817) |
institution |
Open Polar |
collection |
CERN Document Server (CDS) |
op_collection_id |
ftcern |
language |
English |
topic |
Other Fields of Physics |
spellingShingle |
Other Fields of Physics Bueler, E Brown, J On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
topic_facet |
Other Fields of Physics |
description |
This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumulation and heat source functions which make a chosen pair of functions for thickness and temperature into exact solutions of the coupled system. The solution we construct here is ``TestG'' in (Bueler and others, 2006) and the steady state solution ``Test F'' is a special case. In the second section we give a reference C implementation of these exact solutions. In the last section we give an error analysis of a finite difference scheme for the temperature equation in the thermocoupled model. The error analysis gives three results, first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for stability of the advection scheme, second an equation for error growth which contributes to understanding the famous ``spokes'' of (Payne and others, 2000), and third a convergence theorem under stringent fixed geometry and smoothness assumptions. |
author |
Bueler, E Brown, J |
author_facet |
Bueler, E Brown, J |
author_sort |
Bueler, E |
title |
On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
title_short |
On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
title_full |
On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
title_fullStr |
On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
title_full_unstemmed |
On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
title_sort |
on exact solutions and numerics for cold, shallow, and thermocoupled ice sheets |
publishDate |
2006 |
url |
http://cds.cern.ch/record/989975 |
long_lat |
ENVELOPE(167.867,167.867,-72.817,-72.817) |
geographic |
Payne |
geographic_facet |
Payne |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
http://cds.cern.ch/record/989975 physics/0610106 oai:cds.cern.ch:989975 |
_version_ |
1766031351709958144 |