Simulation of Sea-ice Thermodynamics by a Smoothed Particle Hydrodynamics Method

Abstract

The paper deals with the problem of sea-ice pack motion and deformation under the action of wind and water drag forces. Differential equations describing the behaviour of ice, with its very distinct material responses in converging and diverging flows, express the mass and linear momentum balances on a horizontal plane (the free surface of the ocean). The thermodynamic effects (ice melting and lead water freezing) are accounted for by adding source terms to the equations describing the evolution of the ice thickness and area fraction (concentration). These thermodynamic source terms are described by means of a single function that idealizes typical ice growth-rates observed in winter in the Arctic. The equations governing the problem are solved by a fully Lagrangian method of the smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model was used to simulate the flow of a sea-ice pack driven by wind drag stresses and varying seasonal temperatures. The results of numerical simulations illustrate the evolution of an ice pack, including distributions of ice thickness and ice area fraction in space and time for assumed temperature distributions.

Smoothed particle hydrodynamics implementation of the standard viscous–plastic sea-ice model and validation in simple idealized experiments

“…Subsequently, the model could be tested against other benchmark problems in an idealized domain to further understand and compare the effect of the SPH method (Flato, 1993;Hunke, 2001;Hibler et al, 2006;Danilov et al, 2015;Mehlmann et al, 2021). Also, in order to use the model for pan-Arctic simulations, the Coriolis and sea surface tilt force along with the treatment of the thermodynamics source and sink terms should be implemented in the SPH framework (see preliminary work by Staroszczyk, 2018). In addition, the parallelization of the code should be improved in order to bring the computational time down to a value comparable to that of an FDM model.…”

Smoothed Particle Hydrodynamics Implementation of the Standard Viscous-Plastic Sea-Ice Model and Validation in Simple Idealized Experiments

“…For future work, a more physical treatment of the boundary conditions should be investigated -e.g., using the immerse boundary method (Tu et al, 2018) with a fixed grid for the boundary and an interpolation scheme to apply force on the particle to simulate the grounding of sea-ice near the coast. In order to use the model for pan-Arctic simulations, the Coriolis and sea surface tilt force along with the treatment of the thermodynamics source and sink terms should be implemented in the SPH framework (see preliminary work by Staroszczyk, 2018). In addition, the parallelization of the code should be improved in order to bring the computational time down to a value comparable to that of an FDM model.…”

Generalized‐α scheme in the PFEM for velocity‐pressure and displacement‐pressure formulations of the incompressible Navier–Stokes equations

“…This consists of simulating a wave of amplitude $$$ A $$$ propagating in a rectangular container of constant depth $$$ H $$$. Instead of displacing a fluid volume at the beginning of the simulation to generate the wave, another common approach 35,36,54,55 is adopted here: to impose as initial condition the analytical approximation proposed Wehausen and Laitone 56 . Taking their system of equations with second order approximation (eq.…”

“…This is because analytical equations are limited to linear conditions, such as waves with small amplitude $$$ A $$$. As shown in References 55 and 36, the analytical approximations are rather accurate if $$$ A/H\le $$$ 0.1, but less if $$$ A/H\ge $$$ 0.2. Therefore, for error analysis of time integration schemes, the maximum wave height at 40 s of simulation is compared with that obtained from a simulation using a time step $$$ \Delta t=0.00078125 $$$, the GA method $$$ \left({\rho}_{\infty }=0.0\right) $$$ and a discretization with finite elements of 1 m size.…”