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Accurate and stable time stepping in ice sheet modeling
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 329, p. 29-47Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2017. Vol. 329, p. 29-47
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-309278DOI: 10.1016/j.jcp.2016.10.060ISI: 000390511500003OAI: oai:DiVA.org:uu-309278DiVA, id: diva2:1051674
Projects
eSSENCEAvailable from: 2016-11-02 Created: 2016-12-02 Last updated: 2019-09-01Bibliographically approved
In thesis
1. Numerical ice sheet modeling: Forward and inverse problems
Open this publication in new window or tab >>Numerical ice sheet modeling: Forward and inverse problems
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Ice sheets have strong influence on the climate system. Numerical simulation provides a mathematical tool to study the ice dynamics in the past and to predict their contribution to climate change in the future. Large scale ice sheets behave as incompressible non-Newtonian fluid. The evolution of ice sheet is governed by the conservation laws of mass, momentum and energy, which is formulated as a system of partial differential equations. Improving the efficiency of numerical ice sheet modeling is always a desirable feature since many of the applications have large domain and aim for long time span. With such a goal, the first part of this thesis focuses on developing efficient and accurate numerical methods for ice sheet simulation.

A large variety of physical processes are involved in ice dynamics, which are described by physical laws with parameters measured from experiments and field work. These parameters are considered as the inputs of the ice sheet simulations. In certain circumstances, some parameters are unavailable or can not be measured directly. Therefore, the second part of this thesis is devoted to reveal these physical parameters by solving inverse problems.

In the first part, improvements of temporal and spatial discretization methods and a sub-grid boundary treatment are purposed. We developed an adaptive time stepping method in Paper I to automatically adjust the time steps based on stability and accuracy criteria. We introduced an anisotropic Radial Basis Function method for the spatial discretization of continental scale ice sheet simulations in Paper II. We designed a sub-grid method for solving grounding line migration problem with Stokes equations in Paper VI.

The second part of the thesis consists of analysis and numerical experiments on inverse problems. In Paper IV and V, we conducted sensitivity analysis and numerical examples of the inversion on time dependent ice sheet simulations. In Paper III, we solved an inverse problem for the thermal conductivity of firn pack at Lomonosovfonna, Svalbard, using the subsurface temperature measurements.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 43
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1849
Keywords
ice sheet modeling, finite element method, grounding line migration, inverse problems, adjoint method
National Category
Computational Mathematics Geosciences, Multidisciplinary
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-392268 (URN)978-91-513-0738-1 (ISBN)
Public defence
2019-10-18, ITC 2446, Ångströmlaboratoriet, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council Formas, 2013-1600, 2017-00665
Available from: 2019-09-26 Created: 2019-09-01 Last updated: 2019-10-15

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Cheng, GongLötstedt, Pervon Sydow, Lina

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