Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations
A common technique for simulating non–Newtonian fluid dynamics, such as snow avalanches, is to solve the Shallow Water Equations (SWE), together with a rheological model describing the momentum dissipation by shear stresses. Friction and cohesion terms are commonly modelled using the Voellmy frictio...
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ftdoajarticles:oai:doaj.org/article:714943a014504c558ef61a3b2b4f6aa9 2023-08-20T04:07:38+02:00 Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations Marcos Sanz-Ramos Ernest Bladé Pere Oller Glòria Furdada https://doi.org/10.1017/jog.2023.48 https://doaj.org/article/714943a014504c558ef61a3b2b4f6aa9 EN eng Cambridge University Press https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article https://doaj.org/toc/0022-1430 https://doaj.org/toc/1727-5652 doi:10.1017/jog.2023.48 0022-1430 1727-5652 https://doaj.org/article/714943a014504c558ef61a3b2b4f6aa9 Journal of Glaciology, Pp 1-17 2D Shallow Water Equations dense snow avalanches finite volume method non–Newtonian fluid Roe scheme Environmental sciences GE1-350 Meteorology. Climatology QC851-999 article ftdoajarticles https://doi.org/10.1017/jog.2023.48 2023-07-30T00:39:06Z A common technique for simulating non–Newtonian fluid dynamics, such as snow avalanches, is to solve the Shallow Water Equations (SWE), together with a rheological model describing the momentum dissipation by shear stresses. Friction and cohesion terms are commonly modelled using the Voellmy friction model and, recently, the Bartelt cohesion model. Here, an adaptation of the Roe scheme that ensures the balance between the flux and pressure gradients and the friction source term is presented. An upwind scheme was used for the discretisation of the SWE numerical fluxes and the non–velocity-dependent terms of the friction–cohesion model, whereas a centred scheme was used for the velocity-dependent source terms. The model was tested in analytically solvable settings, laboratory experiments and real cases. In all cases, the model performed well, avoiding numerical instabilities and achieving stable and consistent solution even for an avalanche stopping on a sloping terrain. Article in Journal/Newspaper Journal of Glaciology Directory of Open Access Journals: DOAJ Articles Journal of Glaciology 1 17 |
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Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
2D Shallow Water Equations dense snow avalanches finite volume method non–Newtonian fluid Roe scheme Environmental sciences GE1-350 Meteorology. Climatology QC851-999 |
spellingShingle |
2D Shallow Water Equations dense snow avalanches finite volume method non–Newtonian fluid Roe scheme Environmental sciences GE1-350 Meteorology. Climatology QC851-999 Marcos Sanz-Ramos Ernest Bladé Pere Oller Glòria Furdada Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
topic_facet |
2D Shallow Water Equations dense snow avalanches finite volume method non–Newtonian fluid Roe scheme Environmental sciences GE1-350 Meteorology. Climatology QC851-999 |
description |
A common technique for simulating non–Newtonian fluid dynamics, such as snow avalanches, is to solve the Shallow Water Equations (SWE), together with a rheological model describing the momentum dissipation by shear stresses. Friction and cohesion terms are commonly modelled using the Voellmy friction model and, recently, the Bartelt cohesion model. Here, an adaptation of the Roe scheme that ensures the balance between the flux and pressure gradients and the friction source term is presented. An upwind scheme was used for the discretisation of the SWE numerical fluxes and the non–velocity-dependent terms of the friction–cohesion model, whereas a centred scheme was used for the velocity-dependent source terms. The model was tested in analytically solvable settings, laboratory experiments and real cases. In all cases, the model performed well, avoiding numerical instabilities and achieving stable and consistent solution even for an avalanche stopping on a sloping terrain. |
format |
Article in Journal/Newspaper |
author |
Marcos Sanz-Ramos Ernest Bladé Pere Oller Glòria Furdada |
author_facet |
Marcos Sanz-Ramos Ernest Bladé Pere Oller Glòria Furdada |
author_sort |
Marcos Sanz-Ramos |
title |
Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
title_short |
Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
title_full |
Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
title_fullStr |
Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
title_full_unstemmed |
Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equations |
title_sort |
numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2d shallow water equations |
publisher |
Cambridge University Press |
url |
https://doi.org/10.1017/jog.2023.48 https://doaj.org/article/714943a014504c558ef61a3b2b4f6aa9 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology, Pp 1-17 |
op_relation |
https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article https://doaj.org/toc/0022-1430 https://doaj.org/toc/1727-5652 doi:10.1017/jog.2023.48 0022-1430 1727-5652 https://doaj.org/article/714943a014504c558ef61a3b2b4f6aa9 |
op_doi |
https://doi.org/10.1017/jog.2023.48 |
container_title |
Journal of Glaciology |
container_start_page |
1 |
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17 |
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1774719414419062784 |