Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes
A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of these models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an ex...
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ftdoajarticles:oai:doaj.org/article:320773996242453287a3471142e03477 2023-05-15T18:32:27+02:00 Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes A. Simson H. Löwe J. Kowalski 2021-12-01T00:00:00Z https://doi.org/10.5194/tc-15-5423-2021 https://doaj.org/article/320773996242453287a3471142e03477 EN eng Copernicus Publications https://tc.copernicus.org/articles/15/5423/2021/tc-15-5423-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-5423-2021 1994-0416 1994-0424 https://doaj.org/article/320773996242453287a3471142e03477 The Cryosphere, Vol 15, Pp 5423-5445 (2021) Environmental sciences GE1-350 Geology QE1-996.5 article 2021 ftdoajarticles https://doi.org/10.5194/tc-15-5423-2021 2022-12-31T05:02:33Z A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of these models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an explicit numerical solution of the ice mass continuity equation can be circumvented, although with the downside of virtual no flexibility in implementing different coupling schemes for densification, phase changes and transport. As a remedy we consistently recast the numerical core of a snowpack model into an extendable Eulerian–Lagrangian framework for solving the coupled non-linear processes. In the proposed scheme, we explicitly solve the most general form of the ice mass balance using the method of characteristics, a Lagrangian method. The underlying coordinate transformation is employed to state a finite-difference formulation for the superimposed (vapor and heat) transport equations which are treated in their Eulerian form on a moving, spatially non-uniform grid that includes the snow surface as a free upper boundary. This formulation allows us to unify the different existing viewpoints of densification in snow or firn models in a flexible way and yields a stable coupling of the advection-dominated mechanical settling with the remaining equations. The flexibility of the scheme is demonstrated within several numerical experiments using a modular solver strategy. We focus on emerging heterogeneities in (two-layer) snowpacks, the coupling of (solid–vapor) phase changes with settling at layer interfaces and the impact of switching to a non-linear mechanical constitutive law. Lastly, we discuss the potential of the scheme for extensions like a dynamical equation for the surface mass balance or the coupling to liquid water flow. Article in Journal/Newspaper The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 15 12 5423 5445 |
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Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
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topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
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Environmental sciences GE1-350 Geology QE1-996.5 A. Simson H. Löwe J. Kowalski Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of these models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an explicit numerical solution of the ice mass continuity equation can be circumvented, although with the downside of virtual no flexibility in implementing different coupling schemes for densification, phase changes and transport. As a remedy we consistently recast the numerical core of a snowpack model into an extendable Eulerian–Lagrangian framework for solving the coupled non-linear processes. In the proposed scheme, we explicitly solve the most general form of the ice mass balance using the method of characteristics, a Lagrangian method. The underlying coordinate transformation is employed to state a finite-difference formulation for the superimposed (vapor and heat) transport equations which are treated in their Eulerian form on a moving, spatially non-uniform grid that includes the snow surface as a free upper boundary. This formulation allows us to unify the different existing viewpoints of densification in snow or firn models in a flexible way and yields a stable coupling of the advection-dominated mechanical settling with the remaining equations. The flexibility of the scheme is demonstrated within several numerical experiments using a modular solver strategy. We focus on emerging heterogeneities in (two-layer) snowpacks, the coupling of (solid–vapor) phase changes with settling at layer interfaces and the impact of switching to a non-linear mechanical constitutive law. Lastly, we discuss the potential of the scheme for extensions like a dynamical equation for the surface mass balance or the coupling to liquid water flow. |
format |
Article in Journal/Newspaper |
author |
A. Simson H. Löwe J. Kowalski |
author_facet |
A. Simson H. Löwe J. Kowalski |
author_sort |
A. Simson |
title |
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
title_short |
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
title_full |
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
title_fullStr |
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
title_full_unstemmed |
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes |
title_sort |
elements of future snowpack modeling – part 2: a modular and extendable eulerian–lagrangian numerical scheme for coupled transport, phase changes and settling processes |
publisher |
Copernicus Publications |
publishDate |
2021 |
url |
https://doi.org/10.5194/tc-15-5423-2021 https://doaj.org/article/320773996242453287a3471142e03477 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_source |
The Cryosphere, Vol 15, Pp 5423-5445 (2021) |
op_relation |
https://tc.copernicus.org/articles/15/5423/2021/tc-15-5423-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-5423-2021 1994-0416 1994-0424 https://doaj.org/article/320773996242453287a3471142e03477 |
op_doi |
https://doi.org/10.5194/tc-15-5423-2021 |
container_title |
The Cryosphere |
container_volume |
15 |
container_issue |
12 |
container_start_page |
5423 |
op_container_end_page |
5445 |
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1766216560849977344 |