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- 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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| 4. |
- 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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- 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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- 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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- 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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