On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets ...

• Main Authors: Bueler, Ed, Brown, Jed
• Format: Text
• Language: unknown
• Published: arXiv 2006
• Subjects: Geophysics physics.geo-ph; Computational Physics physics.comp-ph; Fluid Dynamics physics.flu-dyn; FOS Physical sciences; Ice Sheet
• Online Access: https://dx.doi.org/10.48550/arxiv.physics/0610106; https://arxiv.org/abs/physics/0610106

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 ... : 16 pages, two C codes; extended appendix to Bueler, Brown, and Lingle, "Exact solutions to the thermocoupled shallow ice approximation: effective tools for verification," submitted to J. Glaciol ...