| 1. |
- Ahlberg, Erik, et al.
(författare)
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"Vi klimatforskare stödjer Greta och skolungdomarna"
- 2019
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Ingår i: Dagens nyheter (DN debatt). - 1101-2447.
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- DN DEBATT 15/3. Sedan industrialiseringens början har vi använt omkring fyra femtedelar av den mängd fossilt kol som får förbrännas för att vi ska klara Parisavtalet. Vi har bara en femtedel kvar och det är bråttom att kraftigt reducera utsläppen. Det har Greta Thunberg och de strejkande ungdomarna förstått. Därför stödjer vi deras krav, skriver 270 klimatforskare.
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| 2. |
- 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. |
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| 5. |
- 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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A numerical study of the validity of Shallow Ice Approximations
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Improving numerical ice sheet models is a very active field of research. In part, this is because ice sheet modelling has gained societal relevance in the context of predictions of future sea level rise. Ice sheet modelling is however also a challenging mathematical and computational subject. Since the exact equations governing ice dynamics, the full Stokes equations, are computationally expensive to solve, approximations are crucially needed for many problems. Shallow ice approximations are a family of approximations derived by asymptotic expansion of the exact equations in terms of the aspect ratio, epsilon. Retaining only the zeroth order terms in this expansion yields the by far most frequently used approximation; the Shallow Ice Approximation (SIA). Including terms up to second order yields the Second Order Shallow Ice Approximation (SOSIA), which is a so-called higher order model. Here, we study the validity and accuracy of shallow ice approximations beyond previous analyses of the SIA. We perform a detailed analysis of the assumptions behind shallow ice approximations, i.e. of the order of magnitude of field variables. We do this by using a numerical solution of the exact equations for ice flow over a sloping, undulating bed. We also construct analytical solutions for the SIA and SOSIA and numerically compute the accuracy for varying epsilon by comparing to the exact solution. We find that the assumptions underlying shallow ice approximations are not entirely appropriate since they do not account for a high viscosity boundary layer developing near the ice surface as soon as small bumps are introduced at the ice base. This boundary layer is thick and has no distinct border. Other existing theories which do incorporate the boundary layer are in better, but not full, agreement with our numerical results. Our results reveal that neither the SIA nor the SOSIA is as accurate as suggested by the asymptotic expansion approach. Also, in SOSIA the ice rheology needs to be altered to avoid infinite viscosity, though both our analytical and numerical solutions show that, especially for high bump amplitudes, the accuracy of the SOSIA is highly sensitive to this alternation. However, by updating the SOSIA solution in an iterative manner, we obtain a model which utilises the advantages of shallow ice approximations, while reducing the disadvantages.
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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 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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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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| 11. |
- 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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| 12. |
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| 13. |
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| 14. |
- Helanow, Christian, 1981-, et al.
(författare)
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Galerkin Least-Squares Stabilization in Ice Sheet Modeling - Accuracy, Robustness, and Comparison to other Techniques
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We investigate the accuracy and robustness of one of the most common methods used in glaciology for the discretization of the p-Stokes equations: equal order finite elements with Galerkin Least-Squares (GLS) stabilization. Furthermore we compare the results to other stabilized methods. We find that the vertical velocity component is more sensitive to the choice of GLS stabilization parameter than horizontal velocity. Additionally, the accuracy of the vertical velocity component is especially important since errors in this component can cause ice surface instabilities and propagate into future ice volume predictions. If the element cell size is set to the minimum edge length and the stabilization parameter is allowed to vary non-linearly with viscosity, the GLS stabilization parameter found in literature is a good choice on simple domains. However, near ice margins the standard parameter choice may result in significant oscillations in the vertical component of the surface velocity. For these cases, other stabilization techniques, such as the interior penalty method, result in better accuracy and are less sensitive to the choice of the stabilization parameter. During this work we also discovered that the manufactured solutions often used to evaluate errors in glaciology are not reliable due to high artificial surface forces at singularities. We perform our numerical experiments in both FEniCS and Elmer/Ice.
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| 15. |
- Helanow, Christian, et al.
(författare)
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Stabilized equal low-order finite elements in ice sheet modeling - accuracy and robustness
- 2018
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Ingår i: Computational Geosciences. - : Springer Science and Business Media LLC. - 1420-0597 .- 1573-1499. ; 22:4, s. 951-974
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the accuracy and robustness of one of the most common methods used in glaciology for finite element discretization of the oe-Stokes equations: linear equal order finite elements with Galerkin least-squares (GLS) stabilization on anisotropic meshes. Furthermore, we compare the results to other stabilized methods. We find that the vertical velocity component is more sensitive to the choice of GLS stabilization parameter than horizontal velocity. Additionally, the accuracy of the vertical velocity component is especially important since errors in this component can cause ice surface instabilities and propagate into future ice volume predictions. If the element cell size is set to the minimum edge length and the stabilization parameter is allowed to vary non-linearly with viscosity, the GLS stabilization parameter found in literature is a good choice on simple domains. However, near ice margins the standard parameter choice may result in significant oscillations in the vertical component of the surface velocity. For these reasons, other stabilization techniques, in particular the interior penalty method, result in better accuracy and are less sensitive to the choice of stabilization parameter. During this work, we also discovered that the manufactured solutions often used to evaluate errors in glaciology are not reliable due to high artificial surface forces at singularities. We perform our numerical experiments in both FEniCS and Elmer/Ice.
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| 16. |
- Kirchner, Nina, et al.
(författare)
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Shallow ice approximation, second order shallow ice approximation, and full Stokes models : A discussion of their roles in palaeo-ice sheet modelling and development
- 2016
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Ingår i: Quaternary Science Reviews. - : Elsevier BV. - 0277-3791 .- 1873-457X. ; 147, s. 136-147
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Tidskriftsartikel (refereegranskat)abstract
- Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models - the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard.
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| 17. |
- Kirchner, Nina, et al.
(författare)
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Shallow ice approximation, second order shallow ice approximation, and full Stokes models : A discussion of their roles in palaeo-ice sheet modelling and development
- 2016
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Ingår i: Quaternary Science Reviews. - : Elsevier BV. - 0277-3791 .- 1873-457X. ; 135, s. 103-114
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Forskningsöversikt (refereegranskat)abstract
- Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models - the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard.
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| 18. |
- Löfgren, André, 1992-, et al.
(författare)
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Increasing Numerical Stability of Mountain Valley Glacier Simulations : Implementation and Testing of Free-Surface Stabilization in Elmer/Ice
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper concerns a numerical stabilization method for free-surface ice flow called the free-surface stabilizationalgorithm (FSSA). In the current study, the FSSA is implemented into the numerical ice-flow software Elmer/Ice and tested onsynthetic two-dimensional (2D) glaciers, as well as on the real-world glacier of Midtre Lovénbreen, Svalbard. For the synthetic2D cases it is found that the FSSA method increases the largest stable time-step size at least by a factor of ten for the case of agently sloping ice surface ( 3◦), and by at least a factor of five for cases of moderately to steeply inclined surfaces ( 6◦ − 12◦) .5Furthermore, the FSSA method increases the overall accuracy for all surface slopes. The largest stable time-step size is foundto be smallest for the case of a low sloping surface, despite having overall smaller velocities. For Midtre Lovénbreen the FSSAmethod doubles the largest stable time-step size, however, the accuracy is in this case slightly lowered in the deeper parts ofthe glacier, while it increases near edges. The implication is that the non-FSSA method might be more accurate at predictingglacier thinning, while the FSSA method is more suitable for predicting future glacier extent. A possible application of the10larger time-step sizes allowed for by the FSSA is for spin-up simulations, where relatively fast changing climate data can beincorporated on short time scales, while the slowly changing velocity field is updated over larger time scales.
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| 19. |
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| 20. |
- Löfgren, André, et al.
(författare)
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Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations
- 2022
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Ingår i: Journal of Computational Physics: X. - : Elsevier BV. - 2590-0552. ; 16
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Tidskriftsartikel (refereegranskat)abstract
- Numerical models for predicting future ice mass loss of the Antarctic and Greenland ice sheets require accurately representing their dynamics. Unfortunately, ice-sheet models suffer from a very strict time-step size constraint, which for higher-order models constitutes a severe bottleneck; in each time step a nonlinear and computationally demanding system of equations has to be solved. In this study, stable time-step sizes are increased for a full-Stokes model by implementing a so-called free-surface stabilization algorithm (FSSA). Previously this stabilization has been used successfully in mantle-convection simulations where a similar viscous-flow problem is solved. By numerical investigation it is demonstrated that instabilities on the very thin domains required for ice-sheet modeling behave differently than on the equal-aspect-ratio domains the stabilization has previously been used on. Despite this, and despite the different material properties of ice, it is shown that it is possible to adapt FSSA to work on idealized ice-sheet domains and increase stable time-step sizes by at least one order of magnitude. The FSSA method presented is deemed accurate, efficient and straightforward to implement into existing ice-sheet solvers.
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| 21. |
- Löfgren, André
(författare)
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Stability of the free-surface problem arising in ice-sheet- and glacier modeling : Numerical investigation and stabilization
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of two papers dealing with a stabilization method for free-surface flows. The method was initially developed to stabilize mantle-convection simulations, but is in this work extended to ice-sheet- and glacier modeling. The objective of this thesis is to assess the method when applied glaciological simulations, with regards to stability and accuracy. It is shown that the method works well and increases stable time-step sizes substantially both for ice-sheet- and glacier simulations, without loss of accuracy. The increased stability properties might be useful for performing long-term simulations and increasing sea-level-rise predictions on a centennial time scale.
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