dorsal/arxiv
View SchemaOn exact solutions and numerics for cold, shallow, and thermocoupled ice sheets
| Authors | Ed Bueler, Jed Brown |
|---|---|
| Categories | |
| ArXiv ID | physics/0610106 |
| URL | https://arxiv.org/abs/physics/0610106 |
| DOI | 10.3189/002214307783258396 |
| Journal | Journal of Glaciology, vol. 53, no. 182, 2007 |
Abstract
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.
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"abstract": "This three section report can be regarded as an extended appendix to (Bueler,\nBrown, and Lingle 2006). First we give the detailed construction of an exact\nsolution to a standard continuum model of a cold, shallow, and thermocoupled\nice sheet. The construction is by calculation of compensatory accumulation and\nheat source functions which make a chosen pair of functions for thickness and\ntemperature into exact solutions of the coupled system. The solution we\nconstruct here is ``TestG\u0027\u0027 in (Bueler and others, 2006) and the steady state\nsolution ``Test F\u0027\u0027 is a special case. In the second section we give a\nreference C implementation of these exact solutions. In the last section we\ngive an error analysis of a finite difference scheme for the temperature\nequation in the thermocoupled model. The error analysis gives three results,\nfirst the correct form of the Courant-Friedrichs-Lewy (CFL) condition for\nstability of the advection scheme, second an equation for error growth which\ncontributes to understanding the famous ``spokes\u0027\u0027 of (Payne and others, 2000),\nand third a convergence theorem under stringent fixed geometry and smoothness\nassumptions.",
"arxiv_id": "physics/0610106",
"authors": [
"Ed Bueler",
"Jed Brown"
],
"categories": [
"physics.geo-ph",
"physics.comp-ph",
"physics.flu-dyn"
],
"doi": "10.3189/002214307783258396",
"journal_ref": "Journal of Glaciology, vol. 53, no. 182, 2007",
"title": "On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets",
"url": "https://arxiv.org/abs/physics/0610106"
},
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