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...

Full description

Saved in:
Bibliographic Details
Main Authors: Marcos Sanz-Ramos, Ernest Bladé, Pere Oller, Glòria Furdada
Format: Article
Language:English
Published: Cambridge University Press 2023-12-01
Series:Journal of Glaciology
Subjects:
Online Access:https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1846127745237516288
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
collection DOAJ
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
id doaj-art-714943a014504c558ef61a3b2b4f6aa9
institution Kabale University
issn 0022-1430
1727-5652
language English
publishDate 2023-12-01
publisher Cambridge University Press
record_format Article
series Journal of Glaciology
spelling doaj-art-714943a014504c558ef61a3b2b4f6aa92024-12-11T10:15:39ZengCambridge University PressJournal of Glaciology0022-14301727-56522023-12-01691646166210.1017/jog.2023.48Numerical modelling of dense snow avalanches with a well-balanced scheme based on the 2D shallow water equationsMarcos Sanz-Ramos0https://orcid.org/0000-0003-2534-0039Ernest Bladé1Pere Oller2Glòria Furdada3Flumen Institute, Universitat Politècnica de Catalunya – International Center for Numerical Methods in Engineering, 08034, Barcelona, SpainFlumen Institute, Universitat Politècnica de Catalunya – International Center for Numerical Methods in Engineering, 08034, Barcelona, SpainGeoNeuRisk, 08024, Barcelona, Spain RISKNAT Research Group, Geomodels Institute, Department of Earth and Ocean Dynamics, Universitat de Barcelona, 08028, Barcelona, SpainRISKNAT Research Group, Geomodels Institute, Department of Earth and Ocean Dynamics, Universitat de Barcelona, 08028, Barcelona, SpainA 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.https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article2D Shallow Water Equationsdense snow avalanchesfinite volume methodnon–Newtonian fluidRoe scheme
spellingShingle 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
Journal of Glaciology
2D Shallow Water Equations
dense snow avalanches
finite volume method
non–Newtonian fluid
Roe scheme
title 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_short 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
topic 2D Shallow Water Equations
dense snow avalanches
finite volume method
non–Newtonian fluid
Roe scheme
url https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article
work_keys_str_mv AT marcossanzramos numericalmodellingofdensesnowavalancheswithawellbalancedschemebasedonthe2dshallowwaterequations
AT ernestblade numericalmodellingofdensesnowavalancheswithawellbalancedschemebasedonthe2dshallowwaterequations
AT pereoller numericalmodellingofdensesnowavalancheswithawellbalancedschemebasedonthe2dshallowwaterequations
AT gloriafurdada numericalmodellingofdensesnowavalancheswithawellbalancedschemebasedonthe2dshallowwaterequations