On a least‐squares finite element formulation for sea ice dynamics

Schröder, Jörg; Nisters, Carina; Ricken, Tim

doi:10.1002/pamm.201800156

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Previous studies on the implementation of the sea ice model have shown that the LSFEM is a promising solution to the numerically stiff problem, cf. [24] and [21]. The resolution of the large gradients in the viscosity function, which can be characterized as localization effects, has to be investigated for convergent meshes.…”

Section: Discussionmentioning

confidence: 99%

“…The time-dependent values of the tracer equations need to be discretized with a suitable time integration scheme. In previous investigations different time integration schemes are elaborated, such as the higher-order Taylor-least-squares scheme based on [22], see [21], and the well known Backward-Euler and Crank-Nicolson schemes, compare to [24] and [21]. In the case of the Taylor-least-squares time integration, higher continuity requirements are imposed on the tracer quantities.…”

Section: Time Discretizationmentioning

confidence: 99%

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Large Scale Sea Ice Modeling – Problems and Perspectives.

Nisters

Schröder

2021

Proc Appl Math and Mech

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The visco-plastic sea ice model based on [7] describes the movement of sea ice over large areas of several thousand square kilometers in time. This model has been considered in many publications and has been extended and adapted by numerically motivated and physically-based approaches. The basic model for the simulation of sea ice circulation considers sea ice velocities and stresses coupled to the field quantities of sea ice thickness and concentration. Two transient advection equations describe the development of sea ice thickness and concentration coupled with sea ice velocity. Furthermore, the viscosity in the constitutive equation is dependent on the sea ice velocities in the sense of a non-Newtonian fluid, which makes the constitutive relationship strongly nonlinear. An extension of the model is, for example, the elasto-visco-plastic constitutive law proposed by [10], which gives numerical stabilization. Recent research on the finite element implementation of the sea ice model is turned to formulations based on the (mixed) Galerkin variation approach, see for example [1] and [20]. Likewise, in [15], [16], and [18] solvers are proposed for the efficient solution of the problem. In this paper, we discuss the obstacles and possibilities of a sea ice model implementation, among others, within a leastsquares finite element method (LSFEM). The mixed LSFEM is well established in fluid mechanics, and a significant advantage of the method is its applicability to first-order systems, see e.g. [12]. Thus, this method leads to stable and robust formulations for non-self-adjoint systems, as they are, for example, for the tracer equations. Based on the results of the Taylor least-squares scheme and a first-order Crank-Nicolson time integrator scheme for the tracer equations, see [21], we discuss here possible steps towards an adequate solution strategy for the complete sea ice model.

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Section: Discussionmentioning

confidence: 99%

Section: Time Discretizationmentioning

confidence: 99%

Large Scale Sea Ice Modeling – Problems and Perspectives.

Nisters

Schröder

2021

Proc Appl Math and Mech

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Simulating sea ice drift in the Southern Ocean incorporating real wind data using the LSFEM

Schwarz

Schröder

2021

Proc Appl Math & Mech

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The viscous‐plastic sea ice model of [2] describes the motion of sea ice on large scales. The numerical model of the sea ice drift considers velocities and stresses and is coupled with the field quantities ice thickness and ice concentration, which are modeled by transient advection equations. Here, the viscosity in sense of a non‐Newtonian fluid depends on velocity gradients, as well as on ice concentration and ice thickness. This leads to a strong nonlinearity of the constitutive model. In [8], we discussed the hurdles of large scale sea ice models and possible solutions of an implementation within a least‐squares finite element method (LSFEM). Previous studies on sea ice model implementations have shown that the LSFEM is a promising solution to the numerically difficult problem, cf. [9] and [7]. In this work, another essential aspect of sea ice research comes into play: embedding real data into the numerical solution is an important field of research in sea ice and ocean modeling. Here, we show a 2D boundary value problem for simulating sea ice drift in the Southern Ocean incorporating real wind data from the ERA‐5 project [1].

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Advancements in sea ice dynamics modeling based on a mixed least‐squares finite element study with nonconforming stress approximation

Hellebrand,

Schwarz,

Schröder

2024

Proc Appl Math and Mech

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The seasonal growth and decay of the (Antarctic) sea ice has great impact on the local as well as the world's climate. Thus, the numerical analysis to forecast the sea ice dynamics with all its impact factors and the mutual influence on the climate is of great interest. This contribution studies the application of the least‐squares finite element method (FEM) to the coupled problem considering the ocean velocity, the stresses, the sea ice concentration, and the sea ice thickness. By using conforming and nonconforming approximation spaces for the stresses, their advantages and disadvantages are shown and discussed.

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On a least‐squares finite element formulation for sea ice dynamics

Cited by 3 publications

References 8 publications

Large Scale Sea Ice Modeling – Problems and Perspectives.

Large Scale Sea Ice Modeling – Problems and Perspectives.

Simulating sea ice drift in the Southern Ocean incorporating real wind data using the LSFEM

Advancements in sea ice dynamics modeling based on a mixed least‐squares finite element study with nonconforming stress approximation

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