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Comparison of numerical schemes for the solution of the advective age equation in ice sheets

Greve, Ralf and Wang, Yongqi and Mügge, Bernd (2002):
Comparison of numerical schemes for the solution of the advective age equation in ice sheets.
In: Annals of Glaciology, International Glacial Society, pp. 487-494, 35, (1), ISSN 0260-3055,
DOI: 10.3189/172756402781817112,
[Online-Edition: http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/34606...],
[Article]

Abstract

A one-dimensional model problem for computation of the age field in ice sheets, which is of great importance for dating deep ice cores, is considered. The corresponding partial differential equation (PDE) is of purely advective (hyperbolic) type, which is notoriously difficult to solve numerically. By integrating the PDE over a space-time element in the sense of a finite-volume approach, a general difference equation is constructed from which a hierarchy of solution schemes can be derived. Iteration rules are given explicitly for central differences, first-, second- and third-order (QUICK) upstreaming as well as modified TVD Lax-Friedrichs schemes (TVDLFs).The performance of these schemes in terms of convergence and accuracy is discussed. Second-order upstreaming, the modified TVDLF scheme with Minmod slope limiter and, with limitations of the accuracy directly at the base, first-order upstreaming prove to be the most suitable for numerical age computations in ice-sheet models.

Item Type: Article
Erschienen: 2002
Creators: Greve, Ralf and Wang, Yongqi and Mügge, Bernd
Title: Comparison of numerical schemes for the solution of the advective age equation in ice sheets
Language: English
Abstract:

A one-dimensional model problem for computation of the age field in ice sheets, which is of great importance for dating deep ice cores, is considered. The corresponding partial differential equation (PDE) is of purely advective (hyperbolic) type, which is notoriously difficult to solve numerically. By integrating the PDE over a space-time element in the sense of a finite-volume approach, a general difference equation is constructed from which a hierarchy of solution schemes can be derived. Iteration rules are given explicitly for central differences, first-, second- and third-order (QUICK) upstreaming as well as modified TVD Lax-Friedrichs schemes (TVDLFs).The performance of these schemes in terms of convergence and accuracy is discussed. Second-order upstreaming, the modified TVDLF scheme with Minmod slope limiter and, with limitations of the accuracy directly at the base, first-order upstreaming prove to be the most suitable for numerical age computations in ice-sheet models.

Journal or Publication Title: Annals of Glaciology
Volume: 35
Number: 1
Publisher: International Glacial Society
Divisions: Study Areas
16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Study Areas > Study Area Mechanic
Date Deposited: 02 Sep 2011 13:09
DOI: 10.3189/172756402781817112
Official URL: http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/34606...
Additional Information:

DOI: 10.3189/172756402781817112

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