A high order cut-cell method for solving the shallow-shelf equations

In this paper we present a novel method for solving the shallow-shelf equations in the presence of grounding lines. The shallow-self equations are a two-dimensional system of nonlinear elliptic PDEs with variable coefficients that are discontinuous across the grounding line, which we treat as a shar...

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Bibliographic Details
Published in:Journal of Computational Science
Main Authors: Thacher, Will, Johansen, Hans, Martin, Daniel
Format: Article in Journal/Newspaper
Language:unknown
Published: eScholarship, University of California 2024
Subjects:
Distributed Computing and Systems Software
Information and Computing Sciences
Artificial Intelligence
Shallow-shelf equations
Ice sheet model
Jump conditions
Grounding line
Cut cell
Embedded boundary
Computation Theory and Mathematics
Information Systems
Applied mathematics
Ice Sheet
Online Access:https://escholarship.org/uc/item/0q79r9zb
https://escholarship.org/content/qt0q79r9zb/qt0q79r9zb.pdf
https://doi.org/10.1016/j.jocs.2024.102319
Description
Summary:In this paper we present a novel method for solving the shallow-shelf equations in the presence of grounding lines. The shallow-self equations are a two-dimensional system of nonlinear elliptic PDEs with variable coefficients that are discontinuous across the grounding line, which we treat as a sharp interface between grounded and floating ice. The grounding line is “reconstructed” from ice thickness and basal topography data to provide necessary geometric information for our cut-cell, finite volume discretization. Our discretization enforces jump conditions across the grounding line and achieves high-order accuracy using stencils constructed with a weighted least-squares method. We demonstrate second and fourth order convergence of the velocity field, driving stress, and reconstructed geometric information.

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