A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
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 thickn...
Published in: | Journal of Advances in Modeling Earth Systems |
---|---|
Main Authors: | , , |
Format: | Text |
Language: | English |
Published: |
John Wiley and Sons Inc.
2021
|
Subjects: | |
Online Access: | http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8459298/ https://doi.org/10.1029/2020MS002277 |
id |
ftpubmed:oai:pubmedcentral.nih.gov:8459298 |
---|---|
record_format |
openpolar |
spelling |
ftpubmed:oai:pubmedcentral.nih.gov:8459298 2023-05-15T16:41:14+02:00 A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution Huth, Alex Duddu, Ravindra Smith, Ben 2021-08-24 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8459298/ https://doi.org/10.1029/2020MS002277 en eng John Wiley and Sons Inc. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8459298/ http://dx.doi.org/10.1029/2020MS002277 © 2021. The Authors. Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. https://creativecommons.org/licenses/by/4.0/This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. CC-BY J Adv Model Earth Syst Research Article Text 2021 ftpubmed https://doi.org/10.1029/2020MS002277 2021-10-03T00:46:08Z 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. Text Ice Sheet Ice Shelf Ice Shelves PubMed Central (PMC) Journal of Advances in Modeling Earth Systems 13 8 |
institution |
Open Polar |
collection |
PubMed Central (PMC) |
op_collection_id |
ftpubmed |
language |
English |
topic |
Research Article |
spellingShingle |
Research Article Huth, Alex Duddu, Ravindra Smith, Ben A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution |
topic_facet |
Research Article |
description |
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 |
Text |
author |
Huth, Alex Duddu, Ravindra Smith, Ben |
author_facet |
Huth, Alex Duddu, Ravindra Smith, Ben |
author_sort |
Huth, Alex |
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 |
John Wiley and Sons Inc. |
publishDate |
2021 |
url |
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8459298/ https://doi.org/10.1029/2020MS002277 |
genre |
Ice Sheet Ice Shelf Ice Shelves |
genre_facet |
Ice Sheet Ice Shelf Ice Shelves |
op_source |
J Adv Model Earth Syst |
op_relation |
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8459298/ http://dx.doi.org/10.1029/2020MS002277 |
op_rights |
© 2021. The Authors. Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. https://creativecommons.org/licenses/by/4.0/This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
op_rightsnorm |
CC-BY |
op_doi |
https://doi.org/10.1029/2020MS002277 |
container_title |
Journal of Advances in Modeling Earth Systems |
container_volume |
13 |
container_issue |
8 |
_version_ |
1766031667309314048 |