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Linear Kinematic Features (LKFs) are found everywhere in the Arctic sea ice cover. They are strongly localized deformations often associated with the formation of leads and pressure ridges. Viscous-plastic sea ice models start to generate…

Numerical Analysis · Mathematics 2021-12-08 C. Mehlmann , S. Danilov , M. Losch , J. F. Lemieux , N. Hutter , T. Richter , P. Blain , E. C. Hunke , P Korn

For the numerical simulation of earth system models, Arakawa grids are largely employed. A quadrilateral mesh is assumed for their classical definition, and different types of grids are identified depending on the location of the…

Computational Physics · Physics 2022-11-10 Giacomo Capodaglio , Mark R. Petersen , Adrian K. Turner , Andrew F. Roberts

We present a stable discretization of sea-ice dynamics on triangular grids that can straightforwardly be coupled to an ocean model on a triangular grid with Arakawa C-type staggering. The approach is based on a nonconforming finite element…

Numerical Analysis · Mathematics 2021-02-04 Carolin Mehlmann , Peter Korn

Finite-difference (FD) modeling of seismic waves in the vicinity of dipping interfaces gives rise to artifacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In…

Geophysics · Physics 2022-01-11 Erik F. M. Koene , Jens Wittsten , Johan O. A. Robertsson

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

Numerical Analysis · Mathematics 2025-12-11 Nils Margenberg , Carolin Mehlmann

Discretization of the equations of Viscous Plastic and Elastic Viscous Plastic (EVP) sea ice dynamics on triangular meshes can be done by placing discrete velocities at vertices, cells or edges. Since there are more cells and edges than…

Numerical Analysis · Mathematics 2022-01-19 S. Danilov , C. Mehlmann , V. Fofonova

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with…

Numerical Analysis · Mathematics 2022-09-13 Longfei Gao , Omar Ghattas , David Keyes

Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…

Numerical Analysis · Mathematics 2023-05-24 Tongtong Li , Anne Gelb , Yoonsang Lee

Sea ice cover in the Arctic and Antarctic is an important indicator of changes in the climate, with important environmental, economic and security consequences. The complexity of the spatio-temporal dynamics of sea ice makes it difficult to…

Dynamical Systems · Mathematics 2019-11-06 James Hogg , Maria Fonoberova , Igor Mezic

A significant fraction (4%-13%) of Antarctic sea ice remains stationary as landfast sea-ice ("fast ice"), typically anchored by grounded icebergs. Current global climate models do not represent fast-ice formation due to iceberg grounding,…

Numerical Analysis · Mathematics 2025-07-29 Carolin Mehlmann , Saskia Kahl

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different…

One important tool at our disposal to evaluate the robustness of Global Circulation Models (GCMs) is to understand the horizontal discretization of the dynamical core under a shallow water approximation. Here, we evaluate the accuracy and…

Fluid Dynamics · Physics 2023-09-25 Fabricio Rodrigues Lapolli , Pedro da Silva Peixoto , Peter Korn

High-resolution regional hindcasting of ocean and sea ice plays an important role in the assessment of shipping and operational risks in the Arctic Ocean. The ice-ocean model NEMO-LIM3 was modified to improve its simulation quality for…

Atmospheric and Oceanic Physics · Physics 2019-10-02 Alexander Hvatov , Nikolay O. Nikitin , Anna V. Kalyuzhnaya , Sergey S. Kosukhin

We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid and nonlinear hyperelastic structure. To begin, we first investigate the accuracy of…

Computational Physics · Physics 2018-08-15 Yulong Li , Yun Zhi Law , Vaibhav Joshi , Rajeev Kumar Jaiman

Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More…

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material…

Numerical Analysis · Mathematics 2022-12-28 Yu-hsuan Shih , Carolin Mehlmann , Martin Losch , Georg Stadler

The size of sea ice floes in the marginal ice zone (MIZ) is a key factor influencing ice coverage, albedo, wave propagation, and ocean--atmosphere energy exchanges. Floe size can be observed by processing visual-range imagery from ships,…

Atmospheric and Oceanic Physics · Physics 2026-02-17 Giulio Passerotti , Alberto Alberello , Marcello Vichi , Luke G. Bennetts , James Bailey , Alessandro Toffoli

Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…

Numerical Analysis · Mathematics 2021-07-29 Edward Caunt

Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a…

Fluid Dynamics · Physics 2022-02-24 Sagy Ephrati , Erwin Luesink , Golo Wimmer , Paolo Cifani , Bernard Geurts

The marginal ice zone is a highly dynamical region where sea ice and ocean waves interact. Large-scale sea ice models only compute domain-averaged responses. As the majority of the marginal ice zone consists of mobile ice floes surrounded…

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