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

• 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

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.