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Adaptive Multigrid Methods for coupled ice sheet and ice shelf models

用于耦合冰盖和冰架模型的自适应多重网格方法

基本信息

批准号：
222181801
负责人：
Professor Dr. Ralf Kornhuber
金额：
--
依托单位：
Arbeitsgruppe Numerik partieller Differentialgleichungen
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/222181801?language=en
关键词：
Adaptive Multigrid Methods coupled ice

项目摘要

For more than one decade, Antarctic ice sheets have been retreating dramatically, and are expected to shrink even more quickly in the future. Recent studies have identified the migration of the grounding line separating the grounded part of ice sheets and the floating part of ice shelves as being a key process controlling marine ice sheet stability. It is also well-known that the grounding line is very sensitive with respect to perturbations. However, existing simulation packages such as PISM are based on uniform finite difference meshes and regularization techniques for the algebraic solution. These features limit the manageable complexity of the underlying model as well as the accessible accuracy of numerical approximation. The goal of this project is to develop efficient and reliable numerical solvers for coupled polythermal ice sheet and ice shelf models that allow for higher accuracy and thus higher predictive capability of numerical simulations of Antarctic icing and deicing than existing codes. We will consider a coupled model based on the so-called shallow ice approximation (SIA) for the slow deformation of ice, and the shallow shelf equation (SSA) for the fast basal sliding. In a second step we will add a Stefan–Signorini model for the ice temperature field. Time discretization of SIA and of the Stefan–Signorini model will be based on the method of characteristics which not only provides stability and mass conservation but also gives rise to symmetric spatial problems which can be formulated in terms of convex minimization. Hence, monotone multigrid or related non-smooth Newton multigrid techniques can be applied for efficient and robust algebraic solution. This approach treats non-smoothness by convexity rather than by regularization. High resolution of the grounding line will be provided throughout the evolution by adaptive mesh refinement based on suitable a posteriori error estimates. Implementations will be carried out in the framework of the finite element environment Dune.

十多年来，南极冰盖一直在急剧消退，预计未来缩小的速度会更快。最近的研究发现，分隔冰盖接地部分和冰架漂浮部分的接地线的迁移是控制海洋冰盖稳定性的关键过程。众所周知，接地线对扰动非常敏感。然而，现有的模拟软件包（例如 PISM）基于统一的有限差分网格和代数解的正则化技术。这些功能限制了底层模型的可管理复杂性以及数值近似的可访问精度。该项目的目标是为耦合的多温冰盖和冰架模型开发高效可靠的数值求解器，与现有代码相比，该求解器能够实现更高的精度，从而使南极结冰和除冰的数值模拟具有更高的预测能力。我们将考虑基于用于冰缓慢变形的所谓浅冰近似（SIA）和用于快速基底滑动的浅架方程（SSA）的耦合模型。第二步，我们将为冰温度场添加 Stefan-Signorini 模型。 SIA 和 Stefan-Signorini 模型的时间离散化将基于特征方法，该方法不仅提供稳定性和质量守恒，而且还产生可以用凸最小化形式表示的对称空间问题。因此，单调多重网格或相关的非光滑牛顿多重网格技术可用于高效且鲁棒的代数解决方案。这种方法通过凸性而不是正则化来处理非平滑性。接地线的高分辨率将在整个演化过程中通过基于适当的后验误差估计的自适应网格细化来提供。实施将在有限元环境 Dune 的框架中进行。

项目成果

期刊论文数量（5）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Steady, Shallow Ice Sheets as Obstacle Problems: Well-Posedness and Finite Element Approximation

稳定的浅冰盖作为障碍问题：适定性和有限元近似

DOI：
10.1137/110856654
发表时间：
2012
期刊：
SIAM J. Appl. Math.
影响因子：
0
作者：
G. Jouvet;E. Bueler
通讯作者：
E. Bueler

Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison

DOI：
10.3189/2013jog12j129
发表时间：
2013-04
期刊：
Journal of Glaciology
影响因子：
3.4
作者：
F. Pattyn;L. Perichon;G. Durand;O. Gagliardini;L. Favier;R. Hindmarsh;T. Zwinger;Mismip d Participants
通讯作者：
F. Pattyn;L. Perichon;G. Durand;O. Gagliardini;L. Favier;R. Hindmarsh;T. Zwinger;Mismip d Participants

An adaptive Newton multigrid method for a model of marine ice sheets