| 1. |
- Ahlkrona, Josefin, et al.
(författare)
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A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling
- 2021
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Ingår i: Journal of Computational Physics: X. - : Elsevier. - 2590-0552. ; 11
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Tidskriftsartikel (refereegranskat)abstract
- In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt.
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| 3. |
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| 4. |
- Ahlkrona, Josefin, et al.
(författare)
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A numerical study of scaling relations for non-Newtonian thin film flows with applications in ice sheet modelling
- 2013
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Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 66:4, s. 417-435
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Tidskriftsartikel (refereegranskat)abstract
- This article treats the viscous, non-Newtonian thin-film flow of ice sheets, governed by the Stokes equations, and the modelling of ice sheets with asymptotic expansion of the analytical solutions in terms of the aspect ratio, which is a small parameter measuring the shallowness of an ice sheet. An asymptotic expansion requires scalings of the field variables with the aspect ratio. There are several, conflicting, scalings in the literature used both for deriving simplified models and for analysis. We use numerical solutions of the Stokes equations for varying aspect ratios in order to compute scaling relations. Our numerically obtained results are compared with three known theoretical scaling relations: the classical scalings behind the Shallow Ice Approximation, the scalings originally used to derive the so-called Blatter-Pattyn equations, and a non-uniform scaling which takes into account a high viscosity boundary layer close to the ice surface. We find that the latter of these theories is the most appropriate one since there is indeed a boundary layer close to the ice surface where scaling relations are different than further down in the ice. This boundary layer is thicker than anticipated and there is no distinct border with the inner layer for aspect ratios appropriate for ice sheets. This makes direct application of solutions obtained by matched asymptotic expansion problematic.
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| 6. |
- Ahlkrona, Josefin, et al.
(författare)
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Accuracy of the zeroth and second order shallow ice approximation : numerical and theoretical results
- 2013
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Ingår i: Geoscientific Model Development Discussions. - : Copernicus GmbH. - 1991-9611 .- 1991-962X. ; 6, s. 4281-4325
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Abstract. In ice sheet modelling, the Shallow Ice Approximation (SIA) and Second Order Shallow Ice Approximation (SOSIA) schemes are approaches to approximate the solution of the full Stokes equations governing ice sheet dynamics. This is done by writing the solution to the full Stokes equations as an asymptotic expansion in the aspect ratio ε, i.e. the quotient between a characteristic height and a characteristic length of the ice sheet. SIA retains the zeroth order terms and SOSIA the zeroth, first, and second order terms in the expansion. Here, we evaluate the order of accuracy of SIA and SOSIA by numerically solving a two dimensional model problem for different values of ε, and comparing the solutions with a finite element solution of the full Stokes equations obtained from Elmer/Ice. The SIA and SOSIA solutions are also derived analytically for the model problem. For decreasing ε, the computed errors in SIA and SOSIA decrease, but not always in the expected way. Moreover, they depend critically on a parameter introduced to avoid singularities in Glen's flow law in the ice model. This is because the assumptions behind the SIA and SOSIA neglect a thick, high viscosity boundary layer near the ice surface. The sensitivity to the parameter is explained by the analytical solutions.
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| 7. |
- Ahlkrona, Josefin, et al.
(författare)
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Accuracy of the zeroth- and second-order shallow-ice approximation - numerical and theoretical results
- 2013
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Ingår i: Geoscientific Model Development. - : Copernicus GmbH. - 1991-959X .- 1991-9603. ; 6:6, s. 2135-2152
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Tidskriftsartikel (refereegranskat)abstract
- In ice sheet modelling, the shallow-ice approximation (SIA) and second-order shallow-ice approximation (SOSIA) schemes are approaches to approximate the solution of the full Stokes equations governing ice sheet dynamics. This is done by writing the solution to the full Stokes equations as an asymptotic expansion in the aspect ratio epsilon, i.e. the quotient between a characteristic height and a characteristic length of the ice sheet. SIA retains the zeroth-order terms and SOSIA the zeroth-, first-, and second-order terms in the expansion. Here, we evaluate the order of accuracy of SIA and SOSIA by numerically solving a two-dimensional model problem for different values of epsilon, and comparing the solutions with afinite element solution to the full Stokes equations obtained from Elmer/Ice. The SIA and SOSIA solutions are also derived analytically for the model problem. For decreasing epsilon, the computed errors in SIA and SOSIA decrease, but not always in the expected way. Moreover, they depend critically on a parameter introduced to avoid singularities in Glen's flow law in the ice model. This is because the assumptions behind the SIA and SOSIA neglect a thick, high-viscosity boundary layer near the ice surface. The sensitivity to the parameter is explained by the analytical solutions. As a verification of the comparison technique, the SIA and SOSIA solutions for a fluid with Newtonian rheology are compared to the solutions by Elmer/Ice, with results agreeing very well with theory.
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| 8. |
- Ahlkrona, Josefin, 1985-
(författare)
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Computational Ice Sheet Dynamics : Error control and efficiency
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated.
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| 9. |
- Ahlkrona, Josefin, et al.
(författare)
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Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology : Description and first applications of the ISCAL method
- 2016
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 308, s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
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| 10. |
- Ahlkrona, Josefin
(författare)
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How much are the greenland and antarctic ice sheets melting?
- 2018
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Ingår i: XRDS: Crossroads, The ACM Magazine for Students. - : Association for Computing Machinery (ACM). - 1528-4972 .- 1528-4980. ; 25:1, s. 42-47
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Designing better simulation software to prepare for a warming world.
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