用于海冰动力学的间断伽辽金离散化方法
A Discontinuous Galerkin discretization for the sea ice dynamics
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中文总结 AI 辅助
本研究提出采用完全间断伽辽金（DG）方法离散Hibler粘性-塑性海冰模型，通过基准测试验证其对海冰变形特征的解析能力，并证明改进的弹性-粘性-塑性（mEVP）格式的理论收敛性。
中文摘要 AI 辅助
海冰动力学在地球气候系统中发挥着关键作用，是天气和气候预测模型的重要组成部分。然而，其数值模拟仍具挑战性，因为海冰呈现出复杂的力学行为，这源于非线性冰流变学以及与外部物理强迫的相互作用。特别是，海冰存在线性运动学特征（LKFs），即与冰间水道张开或压力脊形成等过程相关的窄带强变形。准确表征这些特征十分必要，因为它们会影响热力学过程以及海冰与大气、海洋的交换。但海冰线性运动学特征的数量、位置和结构对空间分辨率以及所选的海冰速度离散化方法高度敏感。本研究采用完全间断伽辽金（DG）表示法，对包括速度场在内的所有变量进行离散化，以此研究Hibler粘性-塑性海冰模型的空间离散化。DG单元能够表征不连续性，同时具备高阶局部多项式逼近能力，这使其非常适合解析复杂的冰变形特征，并确保对网格诱导数值伪影具有鲁棒性。我们采用已建立的海冰动力学基准测试完全DG方法，将所得海冰变形与最先进的离散化方法进行比较。此外，我们研究了改进的弹性-粘性-塑性（mEVP）格式作为伪时间迭代求解器，用于求解粘性-塑性（VP）动量方程的理论收敛性。我们证明了基础连续伪时间动力系统向粘性-塑性形式极限的收敛性，从而为将mEVP用作Hibler VP模型的迭代求解器提供了理论基础。
英文摘要
Sea ice dynamics plays a crucial role in the Earth's climate system, making it an important component of weather and climate prediction models. Its numerical simulation remains challenging, however, as it exhibits complex mechanical behaviors due to a nonlinear ice rheology and interactions with external physical forcings. In particular, sea ice presents linear kinematic features (LKFs), i.e., narrow bands of intense deformation associated with processes such as lead opening or pressure-ridge formation. Accurately representing these features is necessary as they affect thermodynamics and ocean-atmosphere exchange. Yet their number, localization, and structure are highly sensitive to spatial resolution and to the chosen discretization of the sea ice velocity. In this work, we investigate the spatial discretization of Hibler's viscous plastic sea-ice model using a fully discontinuous Galerkin (DG) representation of all variables, including the velocity field. The ability of DG elements to represent discontinuities while having high order local polynomial approximation makes them well suited for resolving the complex ice deformation features, and insuring robustness towards mesh-induced numerical artefacts. We assess the fully DG method using an established sea ice dynamics benchmark and compare the obtained sea ice deformation with state-of-the-art discretizations. Additionally, we study the theoretical convergence of the modified Elastic-Viscous-Plastic (mEVP) formulation as a pseudo-time iterative solver for the viscous-plastic (VP) momentum equations. We prove the convergence of the underlying continuous pseudo-time dynamical system towards the viscous plastic formal limit, thereby providing a theoretical foundation for the use of mEVP as an iterative solver for Hibler's VP model.
