Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ...
In this paper we consider a nonlinear partial differential equation describing heat flow with ice-water phase transition in permafrost soils. Such models and their numerical approximations have been well explored in the applications literature. In this paper we describe a new direction in which the...
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Online Access: | https://dx.doi.org/10.48550/arxiv.2406.11812 https://arxiv.org/abs/2406.11812 |
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ftdatacite:10.48550/arxiv.2406.11812 2024-09-15T18:11:32+00:00 Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... Peszynska, Malgorzata Slugg, Nicholas 2024 https://dx.doi.org/10.48550/arxiv.2406.11812 https://arxiv.org/abs/2406.11812 unknown arXiv Creative Commons Attribution Non Commercial No Derivatives 4.0 International https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode cc-by-nc-nd-4.0 Numerical Analysis math.NA FOS Mathematics Article Preprint article CreativeWork 2024 ftdatacite https://doi.org/10.48550/arxiv.2406.11812 2024-07-03T11:14:10Z In this paper we consider a nonlinear partial differential equation describing heat flow with ice-water phase transition in permafrost soils. Such models and their numerical approximations have been well explored in the applications literature. In this paper we describe a new direction in which the allow relaxation and hysteresis of the phase transition which introduce additional nonlinear terms and complications for the analysis. We present numerical algorithms as well as analysis of the well-posedness and convergence of the fully implicit iterative schemes. The analysis we propose handles the equilibrium, non-equilibrium, and hysteresis cases in a unified way. We also illustrate with numerical examples for a model ODE and PDE. ... Report Ice permafrost DataCite |
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Numerical Analysis math.NA FOS Mathematics |
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Numerical Analysis math.NA FOS Mathematics Peszynska, Malgorzata Slugg, Nicholas Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
topic_facet |
Numerical Analysis math.NA FOS Mathematics |
description |
In this paper we consider a nonlinear partial differential equation describing heat flow with ice-water phase transition in permafrost soils. Such models and their numerical approximations have been well explored in the applications literature. In this paper we describe a new direction in which the allow relaxation and hysteresis of the phase transition which introduce additional nonlinear terms and complications for the analysis. We present numerical algorithms as well as analysis of the well-posedness and convergence of the fully implicit iterative schemes. The analysis we propose handles the equilibrium, non-equilibrium, and hysteresis cases in a unified way. We also illustrate with numerical examples for a model ODE and PDE. ... |
format |
Report |
author |
Peszynska, Malgorzata Slugg, Nicholas |
author_facet |
Peszynska, Malgorzata Slugg, Nicholas |
author_sort |
Peszynska, Malgorzata |
title |
Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
title_short |
Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
title_full |
Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
title_fullStr |
Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
title_full_unstemmed |
Unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
title_sort |
unified analysis of algorithms for equilibrium, non-equilibrium, and hysteresis models of phase transition in permafrost ... |
publisher |
arXiv |
publishDate |
2024 |
url |
https://dx.doi.org/10.48550/arxiv.2406.11812 https://arxiv.org/abs/2406.11812 |
genre |
Ice permafrost |
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Ice permafrost |
op_rights |
Creative Commons Attribution Non Commercial No Derivatives 4.0 International https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode cc-by-nc-nd-4.0 |
op_doi |
https://doi.org/10.48550/arxiv.2406.11812 |
_version_ |
1810449126959087616 |