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

Abstract We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and i...

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Autores principales:	Alex Huth, Ravindra Duddu, Ben Smith
Formato:	article
Lenguaje:	EN
Publicado:	American Geophysical Union (AGU) 2021
Materias:	ice shelves material point method particle method glaciology damage fracture Physical geography GB3-5030 Oceanography GC1-1581
Acceso en línea:	https://doaj.org/article/5abfb71110894afd8cad2fb160d1987c
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spelling	oai:doaj.org-article:5abfb71110894afd8cad2fb160d1987c2021-11-12T07:13:23ZA Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution1942-246610.1029/2020MS002277https://doaj.org/article/5abfb71110894afd8cad2fb160d1987c2021-08-01T00:00:00Zhttps://doi.org/10.1029/2020MS002277https://doaj.org/toc/1942-2466Abstract We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM‐SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub‐element scales, and a weak formulation based on well‐established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1‐D and 2‐D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid‐crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid‐crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM‐SSA framework is viable for the simulation of ice sheet‐shelf evolution and enables boundary tracking and error‐free advection of history or state variables, such as ice thickness or damage.Alex HuthRavindra DudduBen SmithAmerican Geophysical Union (AGU)articleice shelvesmaterial point methodparticle methodglaciologydamagefracturePhysical geographyGB3-5030OceanographyGC1-1581ENJournal of Advances in Modeling Earth Systems, Vol 13, Iss 8, Pp n/a-n/a (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ice shelves material point method particle method glaciology damage fracture Physical geography GB3-5030 Oceanography GC1-1581
spellingShingle	ice shelves material point method particle method glaciology damage fracture Physical geography GB3-5030 Oceanography GC1-1581 Alex Huth Ravindra Duddu Ben Smith A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
description	Abstract We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM‐SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub‐element scales, and a weak formulation based on well‐established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1‐D and 2‐D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid‐crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid‐crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM‐SSA framework is viable for the simulation of ice sheet‐shelf evolution and enables boundary tracking and error‐free advection of history or state variables, such as ice thickness or damage.
format	article
author	Alex Huth Ravindra Duddu Ben Smith
author_facet	Alex Huth Ravindra Duddu Ben Smith
author_sort	Alex Huth
title	A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
title_short	A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
title_full	A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
title_fullStr	A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
title_full_unstemmed	A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
title_sort	generalized interpolation material point method for shallow ice shelves. 1: shallow shelf approximation and ice thickness evolution
publisher	American Geophysical Union (AGU)
publishDate	2021
url	https://doaj.org/article/5abfb71110894afd8cad2fb160d1987c
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A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution

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