A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice...

Area of Science:

• Glaciology and Computational Fluid Dynamics
• Numerical methods for geophysical flows
• Ice sheet and ice shelf dynamics modeling

Background:

• Accurate simulation of ice flow is crucial for understanding climate change impacts.
• Existing methods like the standard material point method (sMPM) suffer from significant grid-crossing errors in shallow shelf approximation (SSA) simulations.
• Tracking ice fronts and grounding lines at high resolution remains a challenge.

Purpose of the Study:

• To develop and validate a novel numerical framework, the generalized interpolation material point method (GIMPM), for simulating ice flow under the shallow shelf approximation (SSA).
• To address limitations of existing methods, particularly grid-crossing errors and difficulties in boundary tracking.
• To enable efficient and accurate advection of state variables without diffusion errors.

Main Methods:

• Implementation of the GIMPM, a particle-based method analogous to the finite element method, for solving SSA equations.
• Development of novel numerical schemes for particle splitting and integration at domain boundaries.
• Comparison of GIMPM-SSA with the standard material point method (sMPM) and a reweighted sMPM using 1-D and 2-D benchmark cases.

Main Results:

• The GIMPM successfully mitigates severe grid-crossing errors inherent in sMPM simulations of SSA.
• The GIMPM demonstrates superior accuracy compared to reweighted sMPM approaches.
• Automated tracking of ice fronts and grounding lines at sub-element scales is achieved.
• Efficient advection of history or internal state variables (e.g., ice thickness, damage) without diffusion errors is confirmed.

Conclusions:

• The GIMPM-SSA framework is a viable and accurate tool for simulating ice sheet-shelf evolution.
• This method offers significant advantages in boundary tracking and error-free advection of state variables.
• The GIMPM represents a substantial advancement for high-fidelity ice flow modeling.