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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| Format: | Article |
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Cambridge University Press
2023-12-01
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| Series: | Journal of Glaciology |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0022143023000485/type/journal_article |
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| 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 |