A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation
The accurate simulation of heat transfer with phase change is a central problem in cryosphere studies. This is because the non-linear behaviour of enthalpy as function of temperature can prevent thermal models of snow, ice, and frozen soil from converging to the correct solution. Existing numerical...
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2021
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Online Access: | https://doi.org/10.5194/tc-15-2541-2021 https://doaj.org/article/54b40306f4924c4598a084314f8be9d7 |
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ftdoajarticles:oai:doaj.org/article:54b40306f4924c4598a084314f8be9d7 2023-05-15T18:32:28+02:00 A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation N. Tubini S. Gruber R. Rigon 2021-06-01T00:00:00Z https://doi.org/10.5194/tc-15-2541-2021 https://doaj.org/article/54b40306f4924c4598a084314f8be9d7 EN eng Copernicus Publications https://tc.copernicus.org/articles/15/2541/2021/tc-15-2541-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-2541-2021 1994-0416 1994-0424 https://doaj.org/article/54b40306f4924c4598a084314f8be9d7 The Cryosphere, Vol 15, Pp 2541-2568 (2021) Environmental sciences GE1-350 Geology QE1-996.5 article 2021 ftdoajarticles https://doi.org/10.5194/tc-15-2541-2021 2022-12-31T06:08:30Z The accurate simulation of heat transfer with phase change is a central problem in cryosphere studies. This is because the non-linear behaviour of enthalpy as function of temperature can prevent thermal models of snow, ice, and frozen soil from converging to the correct solution. Existing numerical techniques rely on increased temporal resolution in trying to keep corresponding errors within acceptable bounds. Here, we propose an algorithm, originally applied to solve water flow in soils, as a method to solve these integration issues with guaranteed convergence and conservation of energy for any time step size. We review common modelling approaches, focusing on the fixed-grid method and on frozen soil. Based on this, we develop a conservative formulation of the governing equation and outline problems of alternative formulations in discretized form. Then, we apply the nested Newton–Casulli–Zanolli (NCZ) algorithm to a one-dimensional finite-volume discretization of the energy–enthalpy formulation. Model performance is demonstrated against the Neumann and Lunardini analytical solutions and by comparing results from numerical experiments with integration time steps of 1 h, 1 d, and 10 d. Using our formulation and the NCZ algorithm, the convergence of the solver is guaranteed for any time step size. With this approach, the integration time step can be chosen to match the timescale of the processes investigated. Article in Journal/Newspaper The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 15 6 2541 2568 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
spellingShingle |
Environmental sciences GE1-350 Geology QE1-996.5 N. Tubini S. Gruber R. Rigon A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
The accurate simulation of heat transfer with phase change is a central problem in cryosphere studies. This is because the non-linear behaviour of enthalpy as function of temperature can prevent thermal models of snow, ice, and frozen soil from converging to the correct solution. Existing numerical techniques rely on increased temporal resolution in trying to keep corresponding errors within acceptable bounds. Here, we propose an algorithm, originally applied to solve water flow in soils, as a method to solve these integration issues with guaranteed convergence and conservation of energy for any time step size. We review common modelling approaches, focusing on the fixed-grid method and on frozen soil. Based on this, we develop a conservative formulation of the governing equation and outline problems of alternative formulations in discretized form. Then, we apply the nested Newton–Casulli–Zanolli (NCZ) algorithm to a one-dimensional finite-volume discretization of the energy–enthalpy formulation. Model performance is demonstrated against the Neumann and Lunardini analytical solutions and by comparing results from numerical experiments with integration time steps of 1 h, 1 d, and 10 d. Using our formulation and the NCZ algorithm, the convergence of the solver is guaranteed for any time step size. With this approach, the integration time step can be chosen to match the timescale of the processes investigated. |
format |
Article in Journal/Newspaper |
author |
N. Tubini S. Gruber R. Rigon |
author_facet |
N. Tubini S. Gruber R. Rigon |
author_sort |
N. Tubini |
title |
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
title_short |
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
title_full |
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
title_fullStr |
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
title_full_unstemmed |
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
title_sort |
method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation |
publisher |
Copernicus Publications |
publishDate |
2021 |
url |
https://doi.org/10.5194/tc-15-2541-2021 https://doaj.org/article/54b40306f4924c4598a084314f8be9d7 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_source |
The Cryosphere, Vol 15, Pp 2541-2568 (2021) |
op_relation |
https://tc.copernicus.org/articles/15/2541/2021/tc-15-2541-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-2541-2021 1994-0416 1994-0424 https://doaj.org/article/54b40306f4924c4598a084314f8be9d7 |
op_doi |
https://doi.org/10.5194/tc-15-2541-2021 |
container_title |
The Cryosphere |
container_volume |
15 |
container_issue |
6 |
container_start_page |
2541 |
op_container_end_page |
2568 |
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1766216580082958336 |