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

Abstract

Abstract. The Viscous-Plastic (VP) rheology with an elliptical yield curve and normal flow rule is implemented in a Lagrangian modelling framework using the Smoothed Particle Hydrodynamics (SPH) meshfree method. Results show, from perturbation analysis of SPH sea-ice dynamic equations, that the classical SPH particle density formulation expressed as a function of sea-ice concentration and mean ice thickness, leads to incorrect plastic wave speed. We propose a new formulation for particle density that gives a plastic wave speed in line with theory. In all cases, the plastic wave in the SPH framework is dispersive and depends on the smoothing length (i.e., the spatial resolution) and on the SPH kernel employed in contrast with its finite difference method (FDM) implementation counterpart. The steady-state solution for the simple 1D ridging experiment is in agreement with the analytical solution within an error of 1 %. SPH is also able to simulate a stable upstream ice arch in an idealized domain representing the Nares Strait in low wind regime (5.3 [m · s−1]) with an ellipse aspect ratio of 2, an average thickness of 1 [m] and free-slip boundary conditions in opposition to the FDM implementation that requires higher shear strength to simulate it. In higher wind regime (7.5 [m · s−1]) no stable ice arches are simulated — unless the thickness is increased — and the ice arch formation showed no dependence on the size of particles contrary to what is observed in the discrete element framework. Finally, the SPH framework is explicit, can take full advantage of parallel processing capabilities and show potential for pan-arctic climate simulations.

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

“…Data availability. Output data from the SPH sea-ice model simulations along with a version of the model used and the analyzing programs are available at https://doi.org/10.5281/zenodo.6950156 (Marquis et al, 2022).…”

SubZero: A Sea Ice Model With an Explicit Representation of the Floe Life Cycle

“…Since the continuous equations of motion are often unknown, DEMs resort to specifying the interaction laws between its elements and strive to calibrate them using macro-scale observations or laboratory experiments (Grima & Wypych, 2011). Another way of simulating fluid motion with known rheology is the Smoothed Particle Hydrodynamics approach that also simulates particle motion but the laws of their interaction are derived from the continuous fluid rheology (Gutfraind & Savage, 1997;Lindsay & Stern, 2004;Marquis et al, 2022;Monaghan, 1992). As such, DEMs present a more general class of models that could simulate media for which corresponding macro-scale rheology might not exist, provided that the interaction laws between its particles could be constrained from observations.…”