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

• Published in: Annals of Glaciology
• Main Authors: Greve, Ralf, Wang, Yongqi, Mügge, Bernd
• Format: Article in Journal/Newspaper
• Language: English
• Published: International Glaciological Society
• Subjects: Ice sheet; Age equation; Dating; Numerical scheme; Finite volume; 452; Annals of Glaciology; Ice Sheet
• Online Access: http://hdl.handle.net/2115/34606; https://doi.org/10.3189/172756402781817112

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 solvenumerically. 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 modifiedTVD Lax-Friedrichs schemes (TVDLFs). The performance of these schemes in terms of convergence and accuracy is discussed. Second-order upstreaming, themodifiedTVDLF 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.